It is well documented that a model for the underlying asset price process that seeks to capture the behaviour of the market prices of vanilla options needs to exhibit both diffusion and jump features. In this paper we assume that the asset price process S is Markov with càdlàg paths and...

It is a widely recognized fact that risk-reversals play a central role in the pricing of derivatives in foreign exchange markets. It is also known that the values of risk-reversals vary stochastically with time. In this paper we introduce a stochastic volatility model with jumps and local...

In this paper we study the joint ruin problem for two insurance companies that divide between them both claims and premia in some specified proportions (modeling two branches of the same insurance company or an insurance and re-insurance company). Modeling the risk processes of the insurance...