Stochastic Differential Equations for Ruin Probabilities

Stochastic Differential Equations for Ruin Probabilities. Møller, C. M. Journal of Applied Probability, 32(1):74–89, 1995. 00030

Paper doi abstract bibtex

The present paper proposes a general approach for finding differential equations to evaluate probabilities of ruin in finite and infinite time. Attention is given to real-valued non-diffusion processes where a Markov structure is obtainable. Ruin is allowed to occur upon a jump or between the jumps. The key point is to define a process of conditional ruin probabilities and identify this process stopped at the time of ruin as a martingale. Using the theory of marked point processes together with the change-of-variable formula or the martingale representation theorem for point processes, we obtain differential equations for evaluating the probability of ruin. Numerical illustrations are given by solving a partial differential equation numerically to obtain the probability of ruin over a finite time horizon.

@article{moller_stochastic_1995,
	title = {Stochastic {Differential} {Equations} for {Ruin} {Probabilities}},
	volume = {32},
	issn = {0021-9002},
	url = {http://www.jstor.org/stable/3214922},
	doi = {10.2307/3214922},
	abstract = {The present paper proposes a general approach for finding differential equations to evaluate probabilities of ruin in finite and infinite time. Attention is given to real-valued non-diffusion processes where a Markov structure is obtainable. Ruin is allowed to occur upon a jump or between the jumps. The key point is to define a process of conditional ruin probabilities and identify this process stopped at the time of ruin as a martingale. Using the theory of marked point processes together with the change-of-variable formula or the martingale representation theorem for point processes, we obtain differential equations for evaluating the probability of ruin. Numerical illustrations are given by solving a partial differential equation numerically to obtain the probability of ruin over a finite time horizon.},
	number = {1},
	journal = {Journal of Applied Probability},
	author = {Møller, Christian Max},
	year = {1995},
	note = {00030},
	pages = {74--89}
}

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