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Ruin problems and myopic portfolio optimization in continuous trading


  • Aase, Knut Kristian


In continuous trading, ruin problems are important for several reasons. ln the first part of the paper a test criterion for bankruptcy is developed. In the present framework one implicitly assumes the investor's wealth to be different from zero, otherwise the model is not well-defined. It is of practical interest to be able to investigate if a certain stationary Markovian financial strategy may lead to ruin. If ruin can occur, its probability is found to satisfy a partial differential equation. In the second part of the paper, a portfolio optimization problem is investigated and solved using Doléans-Dade's exponential formula. The optimality criterion used is to maximize the expected rate of growth. Because of the special structure of the problem, we avoid the Bellman equation. This fact is fortunate, since the Bellman equation is often very complicated to solve analytically.

Suggested Citation

  • Aase, Knut Kristian, 1986. "Ruin problems and myopic portfolio optimization in continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 21(2), pages 213-227, February.
  • Handle: RePEc:eee:spapps:v:21:y:1986:i:2:p:213-227

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    References listed on IDEAS

    1. Bruss, F. T. & Rogers, L. C. G., 1991. "Pascal processes and their characterization," Stochastic Processes and their Applications, Elsevier, vol. 37(2), pages 331-338, April.
    2. Steutel, F. W., 1973. "Some recent results in infinite divisibility," Stochastic Processes and their Applications, Elsevier, vol. 1(2), pages 125-143, April.
    3. Arjas, Elja & Haara, Pentti & Norros, Ikka, 1992. "Filtering the histories of a partially observed marked point process," Stochastic Processes and their Applications, Elsevier, vol. 40(2), pages 225-250, March.
    4. R. Pillai, 1990. "On Mittag-Leffler functions and related distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(1), pages 157-161, March.
    5. Böker, Fred & Serfozo, Richard, 1983. "Ordered thinnings of point processes and random measures," Stochastic Processes and their Applications, Elsevier, vol. 15(2), pages 113-132, July.
    6. Bunge, J. A. & Nagaraja, H. N., 1991. "The distributions of certain record statistics from a random number of observations," Stochastic Processes and their Applications, Elsevier, vol. 38(1), pages 167-183, June.
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    Cited by:

    1. Jun Liu & Francis A. Longstaff & Jun Pan, 2003. "Dynamic Asset Allocation with Event Risk," Journal of Finance, American Finance Association, vol. 58(1), pages 231-259, February.
    2. Dieckmann, Stephan & Gallmeyer, Michael, 2005. "The equilibrium allocation of diffusive and jump risks with heterogeneous agents," Journal of Economic Dynamics and Control, Elsevier, vol. 29(9), pages 1547-1576, September.
    3. Wee, In-Suk, 1999. "Stability for multidimensional jump-diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 80(2), pages 193-209, April.


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