We study the exponential utility indifference valuation of a contingent claim B in an incomplete market driven by two Brownian motions. The claim depends on a nontradable asset stochastically correlated with the traded asset available for hedging. We use martingale arguments to provide upper and...

In the existing literature on barrier options, much effort has been exerted to ensureconvergence through placing the barrier in close proximity to, or directly onto, thenodes of the tree lattice. In this paper we show that this may not be necessary toachieve accurate option price...

This paper complements theoretical studies on the Kelly rule in evolutionary finance by studying a Darwinian model of selection and reproduction in which the diversity of investment strategies is maintained through genetic programming. We find that investment strategies which optimize long-term...

We apply perturbation theory to solve the optimal control problem of an investor with time-additive power utility over intermediate consumption and final wealth. Under general conditions we show existence of a power series representation for the prevailing optimal consumption and investment...

We solve analytically the Merton's problem of an investor with time-additive power utility. For general state dynamics, we prove existence of two power series representations of the relevant optimal policies and value functions, which hold for all admissible risk aversion parameters. We...

A generalized correlated random walk is a process X_k of partial sums of random variables Y_j such that (X,Y) forms a Markov chain. For a sequence X^n of such processes where each Y^n_j takes only two values, we prove weak convergence to a diffusion process whose generator is explicitly...

We study the dynamic utility indifference value process p(X) when the usefulness of X is evaluated via a dynamic monetary concave utility functional (DMCUF) instead of von Neumann/Morgenstern expected utility. A DMCUF is minus a dynamic convex risk measure. The key tools for our investigations...