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| Soumik Pal |
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| Visiting Assistant Professor of Mathematics |
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Web Site Contact Information
Courses & Office Hours |
Education
Ph.D. (2006), Columbia University
Research Area: Probability, stochastic processes, and their applications to mathematical finance
My dissertation topic centered around what is known as convex measures of risk in mathematical finance. Very simply, the problem can be described as follows. Consider any non-negative stochastic process on a finite time interval. This represents random price movements of a share of a certain stock. I enter the market on day zero with a certain financial objective to achieve by the end of the time interval. It has been shown that most of such natural financial objectives induces a convex set of random variables (depending on the objective) which can be called "acceptable" or "riskless" wealths.
Now, on every day, I decide on the number of shares I buy or sell on
that day, and this "strategy" determines the growth of my wealth.
On
the terminal day I would like my wealth to lie inside the set of
acceptable wealths. This naturally raises the question that, starting
with a pre-specified set of acceptable wealths, how much capital I
must invest initially, and then, by what strategy should I trade in
order to hit it. Depending on the situation, the minimum such capital
can be interpreted either as a "price" or as a "capital
requirement" simply as a "measure of risk". The corresponding
strategy can be
seen as an efficient hedging strategy.
My dissertation consists of two parts. In the first, I give theoretical expressions for the capital requirement problem under a general framework of continuous trading, semimartingale price process, and a few restrictions on the convex set of acceptable wealths. In the latter, I take up a more computational approach. I assume discrete trading, and simpler sets of acceptable wealths, and exhibit a Monte-Carlo scheme to evaluate numerical values of near-optimal capital and explicit expressions for the corresponding strategy. It appears to be the first attempt of its kind in the available literature.
Selected Publications
Capital requirement for achieiving acceptability (submitted). http://arxiv.org/abs/math.PR/0601627
Symmetrization of Bernoulli (submitted). http://arxiv.org/abs/math.PR/0601652
Last modified: October 5, 2006