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A Bound on the Probability of Ruin in Merton’s Model
Computational Mathematics and Modeling, 2017zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Morozov, V. V., Babin, V. A.
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Estimation of ruin probabilities
Insurance: Mathematics and Economics, 1977Consider the compound Poisson claim size process generated by a distribution function B. Denote by W(t. x) the finite time non-ruin probability that the company will not be ruined before 1 starting with initial reserve x. Under appropriate conditions on B it is shown that W(t, χ)−W(∞, χ) is basically of the form exp{−θt−υχ}⋯t 32⋯χ for large t, where θ ...
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Ruin Probability for a Portfolio Including Options
Journal of Mathematical Sciences, 2002The author studies a standard \((B,S)\)-market consisting of a risk-free bond, growing exponentially at a fixed rate \(r\), and a stock, having initial value \(s_0\) and evolving stochastically to a value \(s_T\) at expiration date \(T\). At time \(0\), an investor sells different types of call and put options (based on the stock, with strike prices ...
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Bounds for classical ruin probabilities
Insurance: Mathematics and Economics, 1984This paper derives upper and lower bounds for the ruin probability over infinite time. The key observation is that if \(u=k*(1-u),\) then \(v-u=(v- k*(1-v))*(1-u),\) where \((f*g)(x)=\int^{x}_{0}f(x-y)dg(y)\). Applications to sub-exponential distributions are also given.
de Vylder, F., Goovaerts, M.
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Evaluating ruin probabilities: a streamlined approach
2021Summary: This paper deals with the ruin probability evaluation in a classical risk theory model, under different hypotheses about claims distribution. Our approach is totally innovative, and is based on the application of the mean-value theorem to solve the associated Volterra integral equation.
Paolo De Angelis +4 more
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Survival probability and ruin probability of a risk model
Applied Mathematics-A Journal of Chinese Universities, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A class of approximations of ruin probabilities
Scandinavian Actuarial Journal, 1977Abstract We shall in this paper consider approximation of a risk reserve process by a Wiener process. Our main mathematical tool is the theory of weak convergence of probability measures on metric spaces. Today Billingsley (1968) is the standard reference for that theory.
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Scale Functions and Ruin Probabilities
2013The two main results from the previous chapters concerning the law of the maximum and minimum of the Cramer–Lundberg process can now be put to use in order to establish our first results concerning the classical ruin problem. We introduce the so-called scale functions, which will prove to be indispensable, both in this chapter and later, when ...
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