Investing for retirement: Terminal wealth constraints or a desired wealth target?

This paper investigates a robust optimal excess-of-loss reinsurance and investment problem with delay and dependent risks for an ambiguity-averse insurer (AAI). The AAI’s wealth process is assumed to be two dependent classes of insurance business. He/she can purchase excess-of-loss reinsurance from the reinsurer and invest in a risk-free asset and a risky asset whose price follows Heston model. We obtain the explicit expressions of the optimal excess-of-loss reinsurance and investment strategy by maximizing the expected exponential utility of AAI’s terminal wealth. Finally, we give the proof of the verification theorem. Our models and results posed here can be regarded as a generalization of the existing results in the literature.

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Less is more: Increasing retirement gains by using an upside terminal wealth constraint

Insurance Mathematics and Economics ◽

10.1016/j.insmatheco.2015.06.003 ◽

2015 ◽

Vol 64 ◽

pp. 259-267 ◽

Cited By ~ 5

Author(s):

Catherine Donnelly ◽

Russell Gerrard ◽

Montserrat Guillén ◽

Jens Perch Nielsen

Keyword(s):

Less Is More ◽

Terminal Wealth

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Complete Markets (Utility over Terminal Wealth)

Continuous-Time Asset Pricing Theory - Springer Finance ◽

10.1007/978-3-319-77821-1_10 ◽

2018 ◽

pp. 181-201

Author(s):

Robert A. Jarrow

Keyword(s):

Complete Markets ◽

Terminal Wealth

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Dynamic Pricing of General Insurance in a Competitive Market

Astin Bulletin ◽

10.1017/s0515036100014719 ◽

2007 ◽

Vol 37 (1) ◽

pp. 1-34 ◽

Cited By ~ 7

Author(s):

Paul Emms

Keyword(s):

Dynamic Pricing ◽

Insurance Premium ◽

Objective Functions ◽

Insurance Pricing ◽

Terminal Wealth ◽

Optimal Insurance ◽

General Insurance ◽

Discounted Utility ◽

Strategy Changes ◽

Wealth Generation

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.

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OPTIMAL PORTFOLIO UNDER STATE-DEPENDENT EXPECTED UTILITY

International Journal of Theoretical and Applied Finance ◽

10.1142/s0219024918500139 ◽

2018 ◽

Vol 21 (03) ◽

pp. 1850013 ◽

Cited By ~ 1

Author(s):

CAROLE BERNARD ◽

STEVEN VANDUFFEL ◽

JIANG YE

Keyword(s):

Portfolio Choice ◽

Expected Utility ◽

Loss Aversion ◽

Reference Point ◽

Joint Distribution ◽

Optimal Portfolio ◽

Characterization Result ◽

Terminal Wealth ◽

Utility Maximizer ◽

State Dependent

We derive the optimal portfolio for an expected utility maximizer whose utility does not only depend on terminal wealth but also on some random benchmark (state-dependent utility). We then apply this result to obtain the optimal portfolio of a loss-averse investor with a random reference point (extending a result of Berkelaar et al. (2004) Optimal portfolio choice under loss aversion, The Review of Economics and Statistics 86 (4), 973–987). Clearly, the optimal portfolio has some joint distribution with the benchmark and we show that it is the cheapest possible in having this distribution. This characterization result allows us to infer the state-dependent utility function that explains the demand for a given (joint) distribution.

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