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Conditional Value-at-Risk hedging and its applications

  • Author / Creator
    Hongxi, Wan
  • Imposing a constraint on the initial wealth may cause the perfect hedging impossible. In this case, the goal of an investor is to find a strategy that minimize the shortfall under a certain measure, which leads to the concept of partial hedging. In this thesis, the shortfall risk is measured by Conditional Value-at-Risk , a coherent risk measure. We investigate Conditional Value-at-Risk based partial hedging and its applications to equity linked life insurance contracts in different markets. First, we consider a Jump-Diffusion market model with transaction costs. A non-linear partial differential equation that an option value process inclusive of transaction costs should satisfy is provided. In addition, we give the closed-form expression of an European call option price in this market and derive the Conditional Value-at-Risk based partial hedging strategy for it. Our results are implemented to obtain target clients’ survival probabilities and age of equity-linked life insurance contracts. Secondly, we deal with a defaultable Jump-Diffusion market. The minimal superhedging costs of claims with a zero recovery rate are calculated. Moreover, the Conditional Value-at-Risk minimization problem of such defaultable claims is solved successfully by converting it into a static optimization problem in the corresponding default free market. Furthermore, our method is implemented to derive minimal shortfall and optimal hedging strategies of defaultable equity-linked life insurance contracts whose payoffs are equal to the maximum of two risky assets conditioned by the occurrence of a default event. Thirdly, we take a deep look into the first continuous market model in mathematical finance -- the Bachelier model. We introduce two modifications of such a model which are based on SDEs with absorption and reflection. They overcome the drawback of the Bachelier model that is stock prices can take negative values. Comparisons in aspects of perfect hedging price as well as Conditional Value-at-Risk based hedging among the standard Bachelier model, the modified Bachlier model and the Black-Scholes model are executed. In the last part, a risk measure called Range Value-at-Risk that contains Value-at-Risk and Conditional Value-at-Risk as two limiting cases is investigated. We solve the Range Value-at-Risk based partial hedging problem and describe its connections with Value-at-Risk as well as Conditional Value-at-Risk based hedging, which provides a more comprehensive picture about partial hedging. In addition, a numerical example is given to illustrate the application of our methodology in the area of mixed finance/insurance contracts in the market with long-range dependence.

  • Subjects / Keywords
  • Graduation date
    Fall 2021
  • Type of Item
    Thesis
  • Degree
    Doctor of Philosophy
  • DOI
    https://doi.org/10.7939/r3-rj7v-q892
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.