Risk Minimizing Option Pricing in a Semi-Markov Modulated Market

We address risk minimizing option pricing in a semi-Markov modulated market where the floating interest rate depends on a finite state semi-Markov process. The growth rate and the volatility of the stock also depend on the semi-Markov process. Using the Föllmer–Schweizer decomposition we find the locally risk minimizing price for European options and the corresponding hedging strategy. We develop suitable numerical methods for computing option prices.

Portfolio Optimization in a Semi-Markov Modulated Market

We address a portfolio optimization problem in a semi-Markov modulated market. We study both the terminal expected utility optimization on finite time horizon and the risk-sensitive portfolio optimization on finite and infinite time horizon. We obtain optimal portfolios in relevant cases. A numerical procedure is also developed to compute the optimal expected terminal utility for finite horizon problem.

Can a single resource support many consumer species

The conclusion that the number of species co-existing within a biological community cannot exceed the number of limiting factors is not valid if we assume that (i) the relative efficiency of two competing species in utilizing a resource is not independent of the resource density, but one species may be more efficient at a lower density and less efficient at a higher density and (ii) there is a spatial or temporal heterogeneity in the density of the resource. This spatial or temporal heterogeneity does not have to be furnished by factors external to the biological community, but may be generated within the biological community itself as in the case of a vertical gradient of light in a plant community. This possibility of a stable co-existence of more than one species in a community limited by a single resource, even when the resource is being supplied uniformly in space and time, is formally demonstrated.

Asymptotic analysis of option pricing in a Markov modulated market

We address asymptotic analysis of option pricing in a regime switching market where the risk free interest rate, growth rate and the volatility of the stocks depend on a finite state Markov chain. We study two variations of the chain namely, when the chain is moving very fast compared to the underlying asset price and when it is moving very slow. Using quadratic hedging and asymptotic expansion, we derive corrections on the locally risk minimizing option price.