Abstract

This thesis explores robust risk-minimizing hedging strategies for contingent claims in incomplete markets with transaction costs, offering a spectrum of tools to balance risk and cost effectiveness. Robust technique applications to finance and insurance have recently gained popularity due to their ability to mitigate model risk. Model risk arises when strategies (or models) become in and out of sync with the market. A model is robust if it can adapt to a wide range of market-dependent factors. However, robust models can be costly and computationally demanding, especially for complex financial and insurance products. Using a multidimensional event tree model, we employ the asymmetric norm as a semi-robust risk measure, integrating asymmetry for customized risk profiles. Three main strategies are developed: a super-replicating approach ensuring full claim coverage at a higher cost, the norm as constraint, which introduces controlled losses to reduce costs, and the norm as objective, minimizing losses directly to enhance capital efficiency. Additionally, self-financing strategies, which require no additional capital injections, offer cost-effective hedging, while portfolio value as state variable strategies allow real-time adjustments, enhancing robustness under volatile conditions. Testing on European call options show that semi-robust strategies - especially norm-constrained and self-financing approaches - maintain low tail risk with minimized cost, demonstrating versatility in adapting to diverse market conditions, investor goals, and risk tolerances while upholding robust risk control.