The Stochastic Model of Exchange Rates
My area of research this summer is in financial mathematics, which is an applied math that mainly focuses on the financial market. People derive and apply various formulas and models regarding asset pricing, hedging (an investment strategy that offsets the potential losses), and portfolio optimization.
My focus will be on the currency market, and I intend to construct a stochastic model for the most recent exchange rates among various countries. This would involve learning stochastic differential equations and stochastic calculus, in which the functions and the integrals are defined in terms of stochastic processes.
In addition, I will need to study the Wiener process, a continuous-time stochastic process, as well as Ito’s Lemma, an identity used to find the time-dependent function of a stochastic process. The underlying significance of studying the stochastic model for exchange rates is that it helps us forecast the stochastic behavior among different currencies and thus optimizes our time-decision for selling and purchasing currencies.