From ruin theory to pricing reset guarantees and perpetual put options |
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Institution: | 1. Ecole des hautes études commerciales, Université de Lausanne, CH-1015 Lausanne, Switzerland;2. Department of Statistics and Actuarial Science, The University of Iowa, Iowa City, IA 52242, USA;1. School of Automotive Studies & Clean Energy Automotive Engineering Center, Tongji University (Jiading Campus), 4800 Cao''an Road, Shanghai, 201804, PR China;2. Department of Energy Technology, Aalborg University, Denmark |
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Abstract: | We examine the joint distribution of the time of ruin, the surplus immediately before ruin, the deficit at ruin, and the cause of ruin. The time of ruin is analyzed in terms of its Laplace transform, which can naturally be interpreted as discounting. We present two financial applications – the pricing of reset guarantees for a mutual fund or an equity-indexed annuity, and the pricing of a perpetual American put option. In both cases, the logarithm of the price of the underlying asset is modeled as a shifted compound Poisson process. Hence the asset price process has downward discontinuities, with the times and amounts of the drops being random. |
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