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...

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...

The risky assets prices of the bi-variate model are reviewed under the hegemonize concentration filtered physical probability space. In the stochastic variance of the Cox-Ingersoll-Ross process. The Mean-variance hedging expanse on the Föllmer-Schweizer decomposition is stringent to the...

This paper considers binomial approximation of continuous time stochastic processes. It is shown that, under some mild integrability conditions, a process can be approximated in mean square sense and in other strong metrics by binomial processes, i.e., by processes with fixed size binary...

Stochastic volatility models have grown in popularity in the past decade or two. However, for many stochastic volatility models, the functional form of volatility along with the description of the diffusion process for volatility have been posed with analytic convenience in mind. Here, we...

The construction of martingales with given marginal distributions at given times is a recurrent problem in financial mathematics. From a theoretical point of view, this problem is well-known as necessary and sufficient conditions for the existence of such martingales have been described....

Up to the 2007 crisis, research within bottom‐up CDO models mainly concentrated on the dependence between defaults. However, due to the substantial increase in the market price of systemic credit risk protection, more attention has been paid to recovery rate assumptions.In this paper, we focus...

Reformulating the results of del Baño Rollin, Ferreiro-Castilla, and Utzet (2010), we are able to give necessary and sufficient conditions for the moments of the stock price to exist and extend Theorem 2.1 of Forde and Jacquier (2011). Precisely Forde and Jacquier (2011) provide necessary...

This paper reconsiders the predictions of the standard option pricing models in the context of incomplete markets. We relax the completeness assumption of the Black-Scholes (1973) model and as an immediate consequence we can no longer construct a replicating portfolio to price the option....