2,294 research outputs found
Optimal excess-of-loss reinsurance for stochastic factor risk models
We study the optimal excess-of-loss reinsurance problem when both the
intensity of the claims arrival process and the claim size distribution are
influenced by an exogenous stochastic factor. We assume that the insurer's
surplus is governed by a marked point process with dual-predictable projection
affected by an environmental factor and that the insurance company can borrow
and invest money at a constant real-valued risk-free interest rate . Our
model allows for stochastic risk premia, which take into account risk
fluctuations. Using stochastic control theory based on the
Hamilton-Jacobi-Bellman equation, we analyze the optimal reinsurance strategy
under the criterion of maximizing the expected exponential utility of the
terminal wealth. A verification theorem for the value function in terms of
classical solutions of a backward partial differential equation is provided.
Finally, some numerical results are discussed
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Dynamic pricing of general insurance in a competitive market
A model for general insurance pricing is developed which represents a stochastic generalisation of the discrete model proposed by Taylor (1986). This model determines the insurance premium based both on the breakeven premium and the competing premiums offered by the rest of the insurance market. The optimal premium is determined using stochastic optimal control theory for two objective functions in order to examine how the optimal premium strategy changes with the insurer’s objective. Each of these problems can be formulated in terms of a multi-dimensional Bellman equation.
In the first problem the optimal insurance premium is calculated when the insurer maximises its expected terminal wealth. In the second, the premium is found if the insurer maximises the expected total discounted utility of wealth where the utility function is nonlinear in the wealth. The solution to both these problems is built-up from simpler optimisation problems. For the terminal wealth problem with constant loss-ratio the optimal premium strategy can be found analytically. For the total wealth problem the optimal relative premium is found to increase with the insurer’s risk aversion which leads to reduced market exposure and lower overall wealth generation
A BSDE-based approach for the optimal reinsurance problem under partial information
We investigate the optimal reinsurance problem under the criterion of
maximizing the expected utility of terminal wealth when the insurance company
has restricted information on the loss process. We propose a risk model with
claim arrival intensity and claim sizes distribution affected by an
unobservable environmental stochastic factor. By filtering techniques (with
marked point process observations), we reduce the original problem to an
equivalent stochastic control problem under full information. Since the
classical Hamilton-Jacobi-Bellman approach does not apply, due to the infinite
dimensionality of the filter, we choose an alternative approach based on
Backward Stochastic Differential Equations (BSDEs). Precisely, we characterize
the value process and the optimal reinsurance strategy in terms of the unique
solution to a BSDE driven by a marked point process.Comment: 30 pages, 3 figure
Liability-driven investment in longevity risk management
This paper studies optimal investment from the point of view of an investor
with longevity-linked liabilities. The relevant optimization problems rarely
are analytically tractable, but we are able to show numerically that liability
driven investment can significantly outperform common strategies that do not
take the liabilities into account. In problems without liabilities the
advantage disappears, which suggests that the superiority of the proposed
strategies is indeed based on connections between liabilities and asset
returns
Individual Welfare Gains from Deferred Life-Annuities under Stochastic Lee-Carter Mortality
A deferred annuity typically includes an option-like right for the policyholder. At the end of the deferment period, he may either choose to receive annuity payouts, calculated based on a mortality table agreed to at contract inception, or receive the accumulated capital as a lump sum. Considering stochastic mortality improvements, such an option could be of substantial value. Whenever mortality improves less than originally expected, the policyholder will choose the lump sum and buy an annuity on the market granting him a better price. If, however, mortality improves more than expected, the policyholder will choose to retain the deferred annuity. We use a realistically calibrated life-cycle consumption/saving/asset allocation model and calculate the welfare gains of deferred annuities under stochastic Lee- Carter mortality. Our results are relevant both for individual retirement planning and for policymakers, especially if legislation makes annuitization, at least in part, mandatory. Our results also indicate the maximal willingness to pay for the mortality option inherent in deferred annuities, which is of relevance to insurance pricing.Stochastic Mortality, Deferred Annuitization, Retirement Decisions, Annuity Puzzle, Intertemporal Utility Maximization
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