Benchmark Approach to Finance and Insurance
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This chapter introduces a unified continuous time framework for financial and insurance modeling. It is applicable to portfolio optimization, derivative pricing, actuarial pricing and risk measurement when security price processes are modeled via SDEs with jumps. It follows the benchmark approach developed in Platen & Heath (2006). The jumps allow for the modeling of event risk in finance, insurance and other areas. The natural benchmark for asset allocation and the natural numéraire for pricing is represented by the best performing, strictly positive portfolio. This is shown to be the growth optimal portfolio (GOP) which maximizes expected growth. Any nonnegative portfolio, when expressed in units of the GOP, turns out to be a supermartingale. This fundamental property leads to real world pricing which identifies the minimal replicating price. An equivalent risk neutral probability measure need not exist under the benchmark approach, which provides significant freedom for modeling when compared to the classical approach.
KeywordsOption Price Price Formula Bessel Process European Call Option Binomial Tree
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- Platen, E. & Heath, D. (2006). A Benchmark Approach to Quantitative Finance, Springer Finance, Springer. Google Scholar