Bermudan option is an option which allows the holder to exercise at pre-specified time instants where the aim is to maximize expected payoff upon exercise. In most practical cases, the underlying dimensionality of Bermudan options is high and the numerical methods for solving partial...

We discuss the application of gradient methods to calibrate mean reverting stochastic volatility models. For this we use formulas based on Girsanov transformations as well as a modification of the Bismut-Elworthy formula to compute the derivatives of certain option prices with respect to the...

We show that under the Black-Scholes assumption the price of an arithmetic average Asian call option with fixed strike increases with the level of volatility. This statement is not trivial to prove and for other models in general wrong. In fact we demonstrate that in a simple binomial model no...

We combine methods for portfolio optimization in incomplete markets which are due to Karatzas et al. [6] with methods proposed by Nualart based on Malliavin Calculus to model insider trading within a stochastic volatility model. We compute the optimal portfolio within a certain set of insider...

We study the classical real option problem in which an agent faces the decision if and when to invest optimally into a project. The investment is assumed to be irreversible. This problem has been studied by Myers and Majd (Adv Futures Options Res 4:1–21, 1990) for the case of a complete...

This paper investigates an optimal investment problem faced by a defined contribution (DC) pension fund manager under inflationary risk. It is assumed that a representative member of a DC pension plan contributes a fixed share of his salary to the pension fund during the finite time horizon [0,...