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We develop a reduced-form credit risk model with regime-switching intensities to investigate the pricing of a credit default swap (CDS) contract. We assume that the defaults of all the names are driven by some shock events. The arrivals of the shock events and the interest rate are modelled by a multivariate regime-switching shot noise process. We provide the flexibility that the model parameters, including the intensities and the jump sizes of the jump component, can switch over time according to a continuous-time, finite-state Markov chain. The states of the chain may be interpreted as different states of an economy or different stages of a business cycle. Based on the joint Laplace transform of the regime-switching shot noise processes, we derive the explicit formulas for the spreads of CDS contract with and without counterparty risk. Numerical results illustrate changes of market regimes have a significant effect on the spread. [ABSTRACT FROM AUTHOR]

In this paper, we study the pricing of longevity bonds and an insurance contract on multiple lives in a regime-switching market driven by an underlying continuous-time Markov chain. For modeling dependent mortality, we make use of a Markov chain and some shot noise processes with regime switching. By using a martingale method, we give semi-analytical expressions for the price of longevity bonds and the premium of an insurance contract on thekth person to die. [ABSTRACT FROM PUBLISHER]

This paper considers the expected penalty functions for a discrete semi-Markov risk model with randomized dividends. Under the model, individual claims are governed by a Markov chain with finite state space, and the insurer pays a dividend of 1 with a probability at the end of each period if the present surplus is greater than or equal to a threshold value. Recursive formulae and the initial values for the discounted free penalty functions are derived in the two-state model. A numerical example is provided to illustrate the impact of dividend payments on ruin probabilities. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider the survival probability for a discrete semi-Markov risk model, which assumes individual claims are influenced by a Markov chain with finite state space and there is autocorrelation among consecutive claim sizes. Our semi-Markov risk model is similar to the one studied in Reinhard and Snoussi (2001,2002) [1,2] without the restriction imposed on the distributions of the claims. In particular, the model of study includes several existing risk models such as the compound binomial model (with time-correlated claims) and the compound Markov binomial model (with time-correlated claims) as special cases. The main purpose of the paper is to develop a recursive method for computing the survival probability in the two-state model, and present some numerical examples to illustrate the application of our results. [Copyright &y& Elsevier]

This paper considers the compound Markov binomial risk model proposed by Cossette et al. (20032004). Two discrete-time renewal (ordinary renewal and delayed renewal) risk processes associated with the compound Markov binomial risk model are analyzed. Based on the associated ordinary renewal process, a defective renewal equation for the conditional Gerber–Shiu expected discounted penalty function is obtained. The relationship between the conditional expected discounted penalty function in the ordinary renewal case and that in the delayed renewal case is then established. From these results, the conditional ultimate probability of ruin as well as the conditional joint distribution of the surplus just prior to ruin and the deficit at ruin are studied. Finally, it is shown that a modified version of the compound Markov binomial risk model is a special case of the discrete-time semi-Markov risk model introduced by Reinhard and Snoussi (20012002). [ABSTRACT FROM AUTHOR]