Suppose that risk reserves of an insurance company are governed by a Markov-modulated classical risk model with parameters modulated by a finite-state irreducible Markov chain. The main purpose of this paper is to calculate ultimate ruin probability that ruin time, the first time when risk...

A Markov chain with an expanding non-uniform grid matching risk neutral marginal distributions is constructed. Conditional distributions of the chain are in the variance gamma class with prespecified skewness and excess kurtosis. Time change and space scale volatilities are calibrated from...

In this paper we present a fast and accurate algorithm for pricing barrier options in one-dimensional Markov models, including general local volatility models with jumps, L\'evy processes and L\'evy driven SDEs. The approach rests on the construction of an approximating continuous-time Markov...

Trading strategies are valued using non-linear conditional expectations with respect to non-additive probabilities in a discrete time Markovian context. Non-additive probabilities attain conservatism by exaggerating upwards tail loss events and exaggerating downwards tail gain events. Steady...