PsyFi Search

Loading...

Wednesday, 19 December 2012

Experience, Rare Events and Risky Choice

Choice, Education and Experience

Decision making, the challenge of choice, is often discussed as though it’s a single, invariant type of event.  Perhaps this is most strongly presented in the idea of stable preferences, the idea that if we choose to eat the fish at a restaurant one day then we should choose it the next day as well, always assuming we liked it.  People don’t actually behave like this, and decision making is much more complex than economics often makes out.

However, we can roughly divide our choice processes into two – decisions we make from personal experience and decisions we make from education.  We may invest in banks because we've had a good experience doing so, but we may choose to limit our investments based on third-party knowledge that financial institutions are inherently risky.  But how we decide which model to follow can change the course of our lives; and certainly determine the health of our wealth.

The Prospect of Choice

The cornerstone of behavioral economics is Prospect Theory, which applied weightings to the traditional expected-utility models of standard economics.  We've looked at the historical development of this a few times, but we can recap quickly (and if you want a fuller treatment you’ll need to go to the sourced articles).

As we saw in Utility, the Deus Ex-machina of Economics the key to modern economic theory is the idea that people make rational choices – and the definition of rational choice goes way back to discussions between Blaise Pascal and Pierre Fermat in the seventeenth century.  In essence this argues that people should always choose the option that maximizes their expected return, a definition based in probability theory.  However, in the St Petersburg game the probabilities show that the expected return is always greater than the entry price which, under rational choice theory, means that we should always enter the game, no matter how large the entry price. 

However, this is a statement about probabilities - we may be likely to win, but we're not certain to and this uncertainty means that people won't enter the game once the entry fee is above a certain price.  The point is that people don’t really make rational assessments based on probability – there comes a point when the possibility of losing your winnings, even if the probability is low, is too great to be willing to take the chance.  Daniel Bernoulli’s solution to the problem was the idea of expected utility, a subjective form of expected value.  A millionaire may be prepared to gamble the loss of $100,000 on the toss of a coin, but a pauper probably won’t, even if the odds favor them.

Risk and Uncertainty

The idea of expected utility became the central principle of modern economics in the twentieth century but started to run into serious problems when a series of experiments showed that people violated the underlying axioms – so issues such as the Allias Paradox and the Ellsburg Ambiguity Paradox showed that peoples’ choices choices are not independent of the other options available to us (see: Ambiguity Aversion: Investing Under Conditions of Uncertainty).  Choice is affected by uncertainty: people prefer a defined risk to an undefined one.  

This problem was solved in Prospect Theory by Tversky and Kahneman who argued from experimental evidence that people underweight large probability events and overweight small probability ones.  By weighting the probabilities associated with such events Prospect Theory retains the core of Daniel Bernoulli’s great idea of subjective expected utility: and this modification rescued economics by providing an explanation for the various paradoxes that were otherwise so difficult to explain.

All then is well, you would think, in the world of modern economics.  Behavioral psychology has been enlisted to rescue the concept of expected utility and provides an integrated theory for us all to move forward with.  Well, that’s the idea.  However, as we saw in Behavioral Finance’s Smoking Gun, it's possible to set up experiments in a way that shows violations of Prospect Theory – situations where people underweight small probability events rather than overweighting them, for instance.

Experience and Choice

This is a puzzle and one that potentially undermines the whole concept of subjective utility – which would also undermine Prospect Theory and the traditional approach to behavioral economics.  Gerd Gigerenzer has suggested that this can be explained by abandoning the non-empirical theories of modern economics and the vague prescriptions of behavioral economics such as the representative heuristic.  Instead he argues that we should focus on how the brain actually makes decisions.

As an example, Hertwig, Barron, Weber and Erev in Decisions From Experience and the Effect of Rare Events in Risky Choice argue that the inversion of the weighting of small probability events can be explained by looking at how people learn about the likelihood of the occurrence of rare events:
“Decisions from experience and decisions from description can lead to dramatically different choice behavior. In the case of decisions from description, people make choices as if they overweight the probability of rare events, as described by prospect theory. We found that in the case of decisions from experience, in contrast, people make choices as if they underweight the probability of rare events”.
So, for example, if your experience of investing is twenty years of happy share price rises you’ll likely underestimate the chance of a market calamity.  On the other hand if you spend your time reading books about the constantly recurring crashes that dog financial markets you’ll probably overweight the chances of such events. 

Underweighting and Choice

The issue of underweighting from experience is easily drawn out of probability theory.  We will each only experience a relatively small number of events, relative to those in the wider markets.  It's a facet of statistics  that if we only experience a small sample of events relative to the total then we are more than likely to miss the rare event completely – so our experience will not be representative of the probability of the actual event occurring.  Even in large samples recency effects are suspected of causing a similar bias – we’re less likely to have experienced the total failure of one of our investments recently and we’ll tend to discount past events more than recent ones (see: Recency: Hot Hands and the Gambler's Fallacy).

Yet where the researchers examined the effects of decision making from description – i.e. from symbolic information (aka “writing”) – the results obtained matched those found in Prospect Theory.  This fundamental difference in decision making processes based on either experience from limited numbers of samples or from descriptions that require more conscious processing may well be fundamental to understanding the discrepancies at the heart of economics and behavioral finance.

Bifurcated Choice

What’s really interesting, of course, is that neither route actually provides an optimal answer.  The fact that education leads us into a set of biases which can be described by Prospect Theory, while relying on gut instinct leads us into a set of different biases which can’t be, only shows that the underlying theories aren’t very robust: but it doesn’t take us very far down the road of greater understanding.

Still, it’s a start. 



Related articles

99 comments:

  1. The information and the detail were just perfect. I think that your perspective is deep, its just well thought out and really fantastic to see someone.

    ReplyDelete
  2. This comment has been removed by a blog administrator.

    ReplyDelete
  3. associated with such events Prospect Theory retains the core of Daniel Bernoulli’s great idea of subjective expected utility: and this modification rescued economics by providing an explanation for the various paradoxes that were otherwise so difficult to explain.
    herbal incense for sale

    ReplyDelete
  4. Petersburg game the probabilities show that the expected return is always greater than the entry price which, under rational choice theory, means that we should always enter the game, no matter how large the entry price.
    Gallery of Art

    ReplyDelete
  5. rare events, as described by prospect theory. We found that in the case of decisions from experience, in contrast, people make choices as if they underweight the probability of rare events”.
    Dynamics NAV

    ReplyDelete
  6. the chance of a market calamity. On the other hand if you spend your time reading books about the constantly recurring crashes that dog financial markets you’ll probably overweight the chances of such events.
    buy diabetes protocol by dr. kenneth pullman

    ReplyDelete
  7. Tversky and Kahneman who argued from experimental evidence that people underweight large probability events and overweight small probability ones. By weighting the probabilities associated with such events Prospect Theory retains the core of Daniel Bernoulli’s great idea of subjective expected utility: and this modification rescued economics by providing an explanation for the various paradoxes that were otherwise so difficult to explain.
    http://textyourexbackmichaelfiore.com/

    ReplyDelete
  8. abandoning the non-empirical theories of modern economics and the vague prescriptions of behavioral economics such as the representative heuristic. Instead he argues that we should focus on how the brain actually makes decisions.
    how to get a girlfriend model

    ReplyDelete
  9. Even in large samples recency effects are suspected of causing a similar bias – we’re less likely to have experienced the total failure of one of our investments recently and we’ll tend to discount past events more than recent ones (
    https://rebelmouse.com/sensualhunterreviews/

    ReplyDelete
  10. A millionaire may be prepared to gamble the loss of $100,000 on the toss of a coin, but a pauper probably won’t, even if the odds favor them.
    https://www.rebelmouse.com/languageofdesiremichaelfiore/

    ReplyDelete
  11. Even in large samples recency effects are suspected of causing a similar bias – we’re less likely to have experienced the total failure of one of our investments recently and we’ll tend to discount past events more than recent ones
    john rowley old school new body

    ReplyDelete
  12. letely – so our experience will not be representative of the probability of the actual event occurring. Even in large samples recency effects are suspected of causing a similar bias – we’re less likely to have experienced the total failure of one of our investments recently and we’ll tend to discount past events more than recent
    shippers

    ReplyDelete
  13. A fantastic post, i am really thankful to you. This is very helpful in analyzing the website from user point of view.
    Plastic Gauge Isolator

    ReplyDelete
  14. A millionaire may be prepared to gamble the loss of $100,000 on the toss of a coin, but a pauper probably won’t, even if the odds favor them.
    First Oil Painting

    ReplyDelete
  15. However, in the St Petersburg game the probabilities show that the expected return is always greater than the entry price which, under rational choice theory, means that we should always enter the game, no matter how large the entry price.
    pieczątki

    ReplyDelete
  16. Daniel Bernoulli’s solution to the problem was the idea of expected utility, a subjective form of expected value. A millionaire may be prepared to gamble the loss of $100,000 on the toss of a coin, but a pauper probably won’t, even if the odds favor them.

    https://rebelmouse.com/reviewstinnitusmiracle/

    ReplyDelete
  17. Nevertheless YOU will rise up out of the swarm fundamentally by imparting your musings obviously and with conviction. Along these lines, your composed work capacity as well and knowing how to make a school paper can accommodate you an opportunity to surpass desires educationally. essay writing service

    ReplyDelete
  18. I do not post comments on blogs, but I would like to say that this blog really forced me to do so! Thanks, for a really nice read. PVDF Submersible Level Probe

    ReplyDelete
  19. Thank you very much for posting and sharing this great article. It is so interesting. I want to know some other information about this site. So please give me this news quickly. I always will be aware of you.PP Plastic Pressure Gauge

    ReplyDelete
  20. I love commenting on this article and i use to comment here regularly. This article will help me to know in a proper way, thanks for sharing with us.PVDF Plastic Pressure Gauge

    ReplyDelete
  21. This is really a very good article, I am looking for this for long time, but one question right now I have, can I get any new comment to read more.Plastic LED Pressure Gauge

    ReplyDelete
  22. This blog is not just for socializing with others but it can also give us useful information like this. Just like me, I’m a new in this blog and this article gave me lots of ideas.
    PP Plastic LED Pressure Gauge

    ReplyDelete
  23. Hey thanks for sharing this information I have gain lots of different ideas and things. So it’s very useful to us.PVDF Plastic LED Pressure Gauge

    ReplyDelete
  24. This is just the kind of information that i had been looking for, i’am searching so many blog regularly but did not get such as information.
    Plastic LCD Pressure Gauge

    ReplyDelete
  25. Really great effort.Thank you very much This post. Definately help this blog to increase my knowledge.Thanks a lot.PP Plastic LCD Pressure Gauge

    ReplyDelete
  26. This will help me getting good result. If not i will comeback with some quetions .I think you will reply, because i have seen you helping people through reply.PVDF Plastic LCD Presure Gauge

    ReplyDelete
  27. We've looked at the historical development of this a few times, but we can recap quickly (and if you want a fuller treatment you’ll need to go to the sourced articles).
    wordpress portfolio themes

    ReplyDelete
  28. Petersburg game the probabilities show that the expected return is always greater than the entry price which, under rational choice theory, means that we should always enter the game, no matter how large the entry price.
    sicurezza sul lavoro Grosseto

    ReplyDelete
  29. Do you want to learn meditation online? Light Watkins has been providing meditation course from many year in new york.Get the best meditation audio course online and best personal trainer now.

    ReplyDelete
  30. the expected return is always greater than the entry price which, under rational choice theory, means that we should always enter the game, no matter how large the entry price.
    Mark Jones

    ReplyDelete
  31. wonderful information, I had come to know about your blog from my friend, I have read many posts of yours by now, and let me tell you, your website gives the best and the most interesting information.PVDF Plastic LED Presure Gauge

    ReplyDelete
  32. Hey thanks for sharing this information I have gain lots of different ideas and things. So it’s very useful to us.PVDF Plastic LED Pressure Gauge

    ReplyDelete
  33. Wow … Amazing , I hope this post will definetly help me to get some new ideas. Thanks you so much...PP LED Pressure Gauge

    ReplyDelete
  34. This is really a very good article, I am looking for this for long time, but one question right now I have, can I get any new comment to read more.Plastic LED Pressure Gauge

    ReplyDelete
  35. Thank you very much for posting and sharing this great article. It is so interesting. I want to know some other information about this site. So please give me this news quickly. I always will be aware of you.PP Plastic Pressure Gauge

    ReplyDelete
  36. I enjoyed every little bit part of it and I will be waiting for the new updates.Really loved reading your we blog post. The information was very informative and helpful.us.Plastic Pressure Gauge

    ReplyDelete
  37. Nice Information! I am personally appreciate your article. This is a great website. I will make sure that I come back again!.
    Plastic PP Gauge

    ReplyDelete
  38. I recently came across your blog and have been reading along. I thought I would leave my first comment. I don't know what to say except that I have enjoyed reading. Nice blog. I will keep visiting this blog very often.Plastic PVDF Gauge

    ReplyDelete
  39. Spellbound Formula : Mehow From Yahoo TV Reveals His Unusual And Oddly Effective Method For Getting A Man To Feel An Obsessive Need To Commit To You. τραπεζια σαλονιου

    ReplyDelete
  40. then we should choose it the next day as well, always assuming we liked it. People don’t actually behave like this, and decision making is much more complex than economics often makes out.
    Dave Johnson

    ReplyDelete
  41. Great for storing data, I am very excited. Unfortunately this or concepts.

    ReplyDelete
  42. when a series of experiments showed that people violated the underlying axioms – so issues such as the Allias Paradox and the Ellsburg Ambiguity Paradox showed that peoples’ choices choices are not independent of the other options available to us
    analisi di laboratorio roma

    ReplyDelete
  43. I enjoyed every little bit part of it and I will be waiting for the new updates.Really loved reading your we blog post. The information was very informative and helpful.us
    3d Sex Game PC Virtual Aya Full Version (Adult Game English)

    ReplyDelete
  44. either experience from limited numbers of samples or from descriptions that require more conscious processing may well be fundamental to understanding the discrepancies at the heart of economics and behavioral finance.
    Guild Wars 2 Gold

    ReplyDelete
  45. it was my deskie Lise Aferiat's debut of playing the violin part. She has indeed played the Symphonie twice before, but in her other life in the days before joining the Scottish Chamber Orchestra as a harpist!!livelovelaugh

    ReplyDelete
  46. be explained by abandoning the non-empirical theories of modern economics and the vague prescriptions of behavioral economics such as the representative heuristic. Instead he argues that we should focus on how the brain actually makes decisions.
    https://rebelmouse.com/truthfatburningfoodsreview/

    ReplyDelete
  47. Although I would be thrilled to take the first tour you described, it would be worth the trip to see the Mt. Desert gardens alone. If I could get away, I would definitely attend. Perhaps there will be another time. miami dui attorney

    ReplyDelete
  48. problem was the idea of expected utility, a subjective form of expected value. A millionaire may be prepared to gamble the loss of $100,000 on the toss of a coin, but a pauper probably won’t, even if the odds favor them.
    eyki ure

    ReplyDelete
  49. the non-empirical theories of modern economics and the vague prescriptions of behavioral economics such as the representative heuristic. Instead he argues that we should focus on how the brain actually makes decisions.
    teds woodworking package method

    ReplyDelete
  50. he total failure of one of our investments recently and we’ll tend to discount past events more than recent
    low carb

    ReplyDelete
  51. However, in the St Petersburg game the probabilities show that the expected return is always greater than the entry price which, under rational choice theory, means that we should always enter the game, no matter how large the entry price.
    buy instagram followers followfy

    ReplyDelete
  52. I really like the dear information you offer in your articles. I’m able to bookmark your site and show the kids check out up here generally. Im fairly positive theyre likely to be informed a great deal of new stuff here than anyone else!
    purchase instagram followers

    ReplyDelete
  53. option that maximizes their expected return, a definition based in probability theory. However, in the St Petersburg game the probabilities show that the expected return is always greater than the entry price which, under rational choice theory, means that we should always enter the game, no matter how large the entry pric
    how to stop tinnitus from getting worse

    ReplyDelete
  54. However, in the St Petersburg game the probabilities show that the expected return is always greater than the entry price which, under rational choice theory, means that we should always enter the game, no matter how large the entry price.
    make her never want to leave you

    ReplyDelete
  55. By weighting the probabilities associated with such events Prospect Theory retains the core of Daniel Bernoulli’s great idea of subjective expected utility: and this modification rescued economics by providing an explanation for the various paradoxes that were otherwise so difficult to explain.
    best yeast infection treatment at home

    ReplyDelete
  56. which applied weightings to the traditional expected-utility models of standard economics. We've looked at the historical development of this a few times, but we can recap quickly (and if you want a fuller treatment you’ll need to go to the sourced articles).
    curing herpes virus naturally

    ReplyDelete
  57. I really like the dear information you offer in your articles. I’m able to bookmark your site and show the kids check out up here generally. Im fairly positive theyre likely to be informed a great deal of new stuff here than anyone else!
    safe youtube views

    ReplyDelete
  58. But how we decide which model to follow can change the course of our lives; and certainly determine the health of our wealth.
    más info

    ReplyDelete
  59. A very good and informative article indeed . It helps me a lot to enhance my knowledge, I really like the way the writer presented his views. Keep touch with long frocks

    ReplyDelete
  60. A millionaire may be prepared to gamble the loss of $100,000 on the toss of a coin, but a pauper probably won’t, even if the odds favor them.
    https://rebelmouse.com/reviewsgrowtaller4idiots

    ReplyDelete
  61. Daniel Bernoulli’s solution to the problem was the idea of expected utility, a subjective form of expected value. A millionaire may be prepared to gamble the loss of $100,000 on the toss of a coin, but a pauper probably won’t, even if the odds favor them.
    Insurance in Pakistan

    ReplyDelete
  62. However, in the St Petersburg game the probabilities show that the expected return is always greater than the entry price which, under rational choice theory, means that we should always enter the game, no matter how large the entry price.
    rebelmouse

    ReplyDelete
  63. Theory and the traditional approach to behavioral economics. Gerd Gigerenzer has suggested that this can be explained by abandoning the non-empirical theories of modern economics and the vague prescriptions of behavioral economics such as the representative heuristic. Instead he argues that we should focus on how the brain actually makes decisions.
    woodworking plan books

    ReplyDelete
  64. such events Prospect Theory retains the core of Daniel Bernoulli’s great idea of subjective expected utility: and this modification rescued economics by providing an explanation for the various paradoxes that were otherwise so difficult to explain.
    best get your ex back books

    ReplyDelete
  65. I just stumbled upon your blog and wanted to say that I have really enjoyed reading your blog posts. I will contact you for sure for more details, thank you for the advice! Fifa 15 Coins

    ReplyDelete
  66. Theory and the traditional approach to behavioral economics. Gerd Gigerenzer has suggested that this can be explained by abandoning the non-empirical theories of modern economics and the vague prescriptions of behavioral economics such as the representative heuristic. Instead he argues that we should focus on how the brain actually makes decisions.
    https://rebelmouse.com/naturalclearvision/

    ReplyDelete
  67. Thank you very much for posting and sharing this great article. It is so interesting. I want to know some other information about this site. So please give me this news quickly. I always will be aware of you. καναπες

    ReplyDelete
  68. upon your blog and wanted to say that I have really enjoyed reading your blog posts. I will contact you for sure for more details, thank you for the advice!
    about page

    ReplyDelete
  69. this can be explained by abandoning the non-empirical theories of modern economics and the vague prescriptions of behavioral economics such as the representative heuristic.
    how can i cure hypothyroidism naturally

    ReplyDelete
  70. "Global Vox Populi is a leading Market Research Company in India, UAE, China, Singapore, Malaysia, Indonesia, Thailand, Australia, Taiwan, Qatar, Vietnam, Hong Kong, Japan, South Korea, Philippines, Turkey, Oman, Bangladesh, Kuwait, Iran, Bahrain, Colombia, Egypt, Saudi Arabia, Sri Lanka, UK, Germany, Spain, France, Italy, USA and Russia.

    Global Vox Populi (ISO 9001:2008 Certified Company and ESOMAR Corporate Member) is a leading full service market research firm with specialization in Multi-Country Research."

    market research company in india

    ReplyDelete
  71. I found it curious that the most difficult images to read were the ones where the eyes were loaded down with makeup. Cashback

    ReplyDelete
  72. the problem was the idea of expected utility, a subjective form of expected value. A millionaire may be prepared to gamble the loss of $100,000 on the toss of a coin, but a pauper probably won’t, even if the odds favor them.
    https://www.rebelmouse.com/humananatomyandphysiologyguide/

    ReplyDelete
  73. A millionaire may be prepared to gamble the loss of $100,000 on the toss of a coin, but a pauper probably won’t, even if the odds favor them.
    youtube tao of badass

    ReplyDelete
  74. making processes based on either experience from limited numbers of samples or from descriptions that require more conscious processing may well be fundamental to understanding the discrepancies at the heart of economics and behavioral finance.
    gehen Sie hier, um es zu bekommen

    ReplyDelete
  75. Theory and the traditional approach to behavioral economics. Gerd Gigerenzer has suggested that this can be explained by abandoning the non-empirical theories of modern economics and the vague prescriptions of behavioral economics such as the representative heuristic. Instead he argues that we should focus on how the brain actually makes decisions.
    organic garden news

    ReplyDelete
  76. Even in large samples recency effects are suspected of causing a similar bias – we’re less likely to have experienced the total failure of one of our investments recently and we’ll tend to discount past events more than recent ones
    rebelmouse

    ReplyDelete
  77. I love commenting on this article and i use to comment here regularly. This article will help me to know in a proper way, thanks for sharing with us.
    livesex

    ReplyDelete
  78. Locksmith Edmonton deal in variant kinds
    of services which include residential,
    commercial and auto locksmith services.
    If you have got locked out of your car
    and you need emergency services, then
    you can avail our efficient services.

    http://yorklocksmith.com
    http://localedmontonlocksmith.ca

    ReplyDelete
  79. נערות ליווי
    שירותי ליווי
    תסתכל דרך הגלריה של נערות ליווי מלווים שלנו ותראה שזה ארוז מלא של בנות
    מכל רחבי מזרח אירופה. יש לי ליווי ההנאה כדי לקדם מאות מלווים במזרח אירופה באתר שלנו
    ו, של ודאות דבר אחד, אם הם מבולגריה או פולין, לטביה, ליטא ורוסיה, כל מה שהם צריכים
    שהיכולת לרצות את אדם בכל מיני דרכים אישיות ואינטימיות. בין אם אתה מחפש בלונדיני

    ReplyDelete
  80. On the other hand if you spend your time reading books about the constantly recurring crashes that dog financial markets you’ll probably overweight the chances of such events.
    Chicago Escorts

    ReplyDelete
  81. the non-empirical theories of modern economics and the vague prescriptions of behavioral economics such as the representative heuristic. Instead he argues that we should focus on how the brain actually makes decisions.
    http://theofficialwebsite.co/dr-david-desire-system-review

    ReplyDelete
  82. A fantastic post, i am really thankful to you. This is very helpful in analyzing the website from user point of view.

    basics

    ReplyDelete
  83. On the other hand if you spend your time reading books about the constantly recurring crashes that dog financial markets you’ll probably overweight the chances of such events.
    textyourexbackforum.com

    ReplyDelete
  84. with so many tel aviv escort agencies to choose from, each promoting a gorgeous
    array of tel aviv escort girls, are there any benefits of choosing to use one
    particular escort agency on a regular basis?

    http://mysaite.ru

    ReplyDelete
  85. which can’t be, only shows that the underlying theories aren’t very robust: but it doesn’t take us very far down the road of greater understanding.
    rebelmouse

    ReplyDelete
  86. MyOneSpy is a cell phone Monitoring Software. It offer Monitor the Cell phone. It Monitors Android, Black Berry and Iphone Ios Mobiles Phones.
    To Get It Visit:- http://www.myonespy.com

    ReplyDelete
  87. On the other hand if you spend your time reading books about the constantly recurring crashes that dog financial markets you’ll probably overweight the chances of such events.
    girlsdoporn

    ReplyDelete
  88. limit our investments based on third-party knowledge that financial institutions are inherently risky. But how we decide which model to follow can change the course of our lives; and certainly determine the health of our wealth.
    girlsdoporn

    ReplyDelete
  89. which can’t be, only shows that the underlying theories aren’t very robust: but it doesn’t take us very far down the road of greater understanding.
    bubblegum casting

    ReplyDelete
  90. En fait la gauche nous a au moins autant foutu dans la merde que la droite , alors il faudrait peut-être arrêter de faire de la politique comme le font les pseudo rebelles à deux balles. Halong bay cruise

    ReplyDelete
  91. This is definitely the case with stone mantels, and metal antique mantels or reproductions.compuchlor salt cell

    ReplyDelete
  92. I love so much that kind of picture. Very hard word but still natural. Keep me calm
    http://jamtanganonline.com

    ReplyDelete
  93. I'm really happy to find this site and did enjoy reading useful articles posted here. The ideas of the author was awesome, thanks for the share.forex cash rebate

    ReplyDelete