In this paper we develop several regression algorithms for solving general stochastic optimal control problems via Monte Carlo. This type of algorithms is particularly useful for problems with high-dimensional state space and complex dependence structure of the underlying Markov process with...

This chapter introduces the reader to definitions and key properties of stochastic processes that are important in finance. The discussion starts from the description of Brownian motion that describes the idea of a continuous random walk and proceeds to Ito processes that incorporate both trend...

This paper develops the idea of renewal time sampling, a novel sampling scheme constructed from stopping times of semimartingales. Based on this new sampling scheme we propose a class of volatility estimators named renewal based volatility estimators. In this paper we show that: (1) The spot...

Managing large-scale systems often involves simultaneously solving thousands of unrelated stochastic optimization problems, each with limited data. Intuition suggests one can decouple these unrelated problems and solve them separately without loss of generality. We propose a novel data-pooling...

A fundamental alternative for stochastic optimization problems named focus programming is proposed based on the focus theory of choice. Different from the existing approaches such as chance-constrained programming and two-stage stochastic programming which are based on expected utility theory,...

We describe a broad setting under which, for European options, if the underlying asset form a geometric random walk then, the error with respect to the Black-Scholes model converges to zero at a speed of 1/n for continuous payoffs functions, and at a speed of 1/√n for discontinuous payoffs...