5 Stochastic Differential Equations Page 1 5 Stochastic Differential Equations 5.1 Examples
and Some Solution Methods We now return to the possible solutions Xt(ω) of the stochastic …

Mathematical finance has grown into a huge area of research which requires a lot of care
and a large number of sophisticated mathematical tools. The subject draws upon quite …

The purpose of this paper is to develop a fractional white noise calculus and to apply this to
markets modeled by (Wick–) Itô type of stochastic differential equations driven by fractional …

Stochastic control is one of the methods being used to find optimal decision-making
strategies in fields such as operations research and mathematical finance. In recent years …

In this article we develop an explicit formula for pricing European options when the
underlying stock price follows nonlinear stochastic functional differential equations with fixed …

In modern financial practice, asset prices are modelled by means of stochastic processes.
Continuous-time stochastic calculus thus plays a central role in financial modelling. The …

This paper studies the convergence problem for mean field games with common noise. We
define a suitable notion of weak mean field equilibria, which we prove captures all …

In this book, we study stochastic volatility models and methods of pricing, hedging, and
estimation. Among models, we will study models with heavy tails and long memory or long …

This paper deals with an extension of Merton's optimal investment problem to a
multidimensional model with stochastic volatility and portfolio constraints. The classical …

The Mathematics of Finance has become a hot topic in applied mathematics ever since the
discovery of the Black-Scholes option pricing formulas in 1973. Unfortunately, there are very …