Search results for "Complete market"

showing 3 items of 13 documents

A Quasilinear Parabolic Equation with Quadratic Growth of the Gradient modeling Incomplete Financial Markets

2004

We consider a quasilinear parabolic equation with quadratic gradient terms. It arises in the modeling of an optimal portfolio which maximizes the expected utility from terminal wealth in incomplete markets consisting of risky assets and non-tradable state variables. The existence of solutions is shown by extending the monotonicity method of Frehse. Furthermore, we prove the uniqueness of weak solutions under a smallness condition on the derivatives of the covariance matrices with respect to the solution. The in influence of the non-tradable state variables on the optimal value function is illustrated by a numerical example.

Quadratic growthState variableQuadratic equationIncomplete marketsBellman equationMathematical analysisMonotonic functionUniquenessCovarianceQuasilinear PDE quadratic gradient existence and uniqueness of solutions optimal portfolio incomplete marketMathematicsSSRN Electronic Journal
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Pricing Reinsurance Contracts

2011

Pricing and hedging insurance contracts is hard to perform if we subscribe to the hypotheses of the celebrated Black and Scholes model. Incomplete market models allow for the relaxation of hypotheses that are unrealistic for insurance and reinsurance contracts. One such assumption is the tradeability of the underlying asset. To overcome this drawback, we propose in this chapter a stochastic programming model leading to a superhedging portfolio whose final value is at least equal to the insurance final liability. A simple model extension, furthermore, is shown to be sufficient to determine an optimal reinsurance protection for the insurer: we propose a conditional value at risk (VaR) model p…

ReinsuranceExpected shortfallReinsurance Option pricing Incomplete marketsSettore SECS-S/06 -Metodi Mat. dell'Economia e d. Scienze Attuariali e Finanz.Financial economicsInsurance policyIncomplete marketsEconomicsPortfolioBlack–Scholes modelAsset (economics)Mathematical economicsStochastic programming
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Evaluation of Insurance Products with Guarantee in Incomplete Markets

2008

Abstract Life insurance products are usually equipped with minimum guarantee and bonus provision options. The pricing of such claims is of vital importance for the insurance industry. Risk management, strategic asset allocation, and product design depend on the correct evaluation of the written options. Also regulators are interested in such issues since they have to be aware of the possible scenarios that the overall industry will face. Pricing techniques based on the Black & Scholes paradigm are often used, however, the hypotheses underneath this model are rarely met. To overcome Black & Scholes limitations, we develop a stochastic programming model to determine the fair price of the mini…

Statistics and ProbabilityIncomplete marketsEconomics and EconometricsActuarial sciencebusiness.industryOption pricingLife insurance; Policies with minimum guarantee; Option pricing; Incomplete marketsLife insuranceStochastic programmingKey person insurancePolicies with minimum guaranteeSettore SECS-S/06 -Metodi Mat. dell'Economia e d. Scienze Attuariali e Finanz.Valuation of optionsFair valueLife insuranceIncomplete marketsEconomicsAuto insurance risk selectionStatistics Probability and UncertaintybusinessRisk management
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