Mathematical Modelling and Problem Solving in Finance and Insurance

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This proposed research program aims to develop advanced mathematical models of financial and insurance problems to help cope with future financial crises by mitigating the negative effects they will have on society. My research program has four major research directions: 1) the modelling, pricing, securitization, and management of the financial risks associated with increasing longevity; 2) pricing and hedging financial instruments in the presence of liquidity costs; 3) studying financial and insurance problems with different financial/actuarial regimes such as bull and bear market regimes. The long term objective of my research program is integrating the three research directions. Longevity risk refers to situations when pension funds do not have enough money to pay the retiree due to increased longevity. The management of longevity risk is crucial for society, especially in maintaining the stability of the financial and pension system. The design of longevity risk transfer financial instruments such as longevity linked derivatives is of paramount importance because the insurance industry alone can not handle this risk. Therefore, there is a need for mathematical models to price such financial instruments. Classical asset pricing theory assumes that traders act as price takers, that is, they have no impact on the prices paid or received. The relaxation of this assumption leads to price impacts on realized returns, which are refer to as liquidity costs. In the presence of liquidity costs the pricing of an option becomes more involved since one has to find out the liquidity effects on the option price. Regime switching refers to situations when the characteristics of mathematical financial/actuarial models are affected by several regimes (e.g. non crisis versus crisis regimes). The regime switching is consistent with some cyclicality observed in financial and actuarial data. The longevity risk and the mishandling of liquidity costs may trigger the next financial crisis. The main innovative aspect of this research program is the skillful application of appropriate mathematical techniques to societal problems such as the longevity risk, a current and pressing issue. The impact of this research proposal will be in mitigating the negative effects on society of future financial crises. This is done by: 1) designing and pricing of new financial instruments to mitigate risk (e.g. longevity bonds that will lessen longevity risk), 2) providing accurate valuation/pricing of financial derivatives (through incorporating the liquidity costs effects), and 3) considering market switching regimes modelling (such as crisis versus non crisis) which in turn would lead to a more accurate estimation of financial crises effects.      In general previous models seemed to have overlooked designing and pricing risk mitigating financial instruments in the context of liquidity costs and market switching regimes. HQP will be included in this research program.