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On the ruin probabilities in a general economic environment

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  • Nyrhinen, Harri

Abstract

Let {An n=1,2,...} and {Bn n=1,2,...} be sequences of random variables andYn=B1+A1B2+A1A2B3+...+A1...An-1Bn.Let M be a positive real number. Define the time of ruin by TM=inf{n Yn>M} (TM=+[infinity], if Yn[less-than-or-equals, slant]M for n=1,2,...). We are interested in the ruin probabilities for large M. We assume that the sequences {An} and {Bn} are independent and that the variables A1,A2,... are strictly positive. The sequences are allowed to be general in other respects. Our main objective is to give reasons for the crude estimate P(TM

Suggested Citation

  • Nyrhinen, Harri, 1999. "On the ruin probabilities in a general economic environment," Stochastic Processes and their Applications, Elsevier, vol. 83(2), pages 319-330, October.
    • Handle: RePEc:eee:spapps:v:83:y:1999:i:2:p:319-330
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    References listed on IDEAS

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    1. Paulsen, Jostein, 1998. "Ruin theory with compounding assets -- a survey," Insurance: Mathematics and Economics, Elsevier, vol. 22(1), pages 3-16, May.
    2. Paulsen, Jostein, 1998. "Sharp conditions for certain ruin in a risk process with stochastic return on investments," Stochastic Processes and their Applications, Elsevier, vol. 75(1), pages 135-148, June.
    3. Gjessing, Håkon K. & Paulsen, Jostein, 1997. "Present value distributions with applications to ruin theory and stochastic equations," Stochastic Processes and their Applications, Elsevier, vol. 71(1), pages 123-144, October.
    4. Paulsen, Jostein, 1993. "Risk theory in a stochastic economic environment," Stochastic Processes and their Applications, Elsevier, vol. 46(2), pages 327-361, June.
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