This paper investigates the valuation of European option with credit risk in a reduced form model when the stock price is driven by the so-called Markov-modulated jump-diffusion process, in which the arrival rate of rare events and the volatility rate of stock are controlled by a continuous-time Markov chain. We also assume that the interest rate and the default intensity follow the Vasicek models whose parameters are governed by the same Markov chain. We study the pricing of European option and present numerical illustrations.
In this paper, we consider the Markov-dependent risk model with multi-layer dividend strategy and investment interest under absolute ruin, in which the claim occurrence and the claim amount are regulated by an external discrete time Markov chain. We derive systems of integro-differential equations satisfied by the moment-generating function, the nth moment of the discounted dividend payments prior to absolute ruin and the Gerber-Shiu function. Finally, the matrix form of systems of integro-differential equations satisfied by the Gerber-Shiu function is presented.
In this paper, we consider a bisexual Galton-Watson branching process whose offspring probability distribution is controlled by a random environment process. Some results for the probability generating functions associated with the process are obtained and sufficient conditions for certain extinction and for non-certain extinction are established.
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