An optimal investment strategy with maximal risk aversion and its ruin probability

Fernández, Begoña; Hernández–Hernández, Daniel; Meda, Ana; Saavedra, Patricia

doi:10.1007/s00186-007-0191-8

Cited by 16 publications

(17 citation statements)

References 10 publications

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“…In previous articles (Fernández et al 2008;Yang and Zhang 2005), the asset price was modeled by a geometric Brownian motion given by…”

Section: The Stochastic Volatility Modelmentioning

confidence: 99%

“…A general verification theorem was proved as well as an existence and uniqueness theorem, which led to a closed form of the optimal strategy, when the correlation factor is equal to zero (ρ = 0). Recently Hata and Yasuda (2017) introduced an extension of (Badaoui and Fernández (2013), Fernández et al (2008)) by considering a multidimensional linear Gaussian stochastic-factor model. They produce an explicit optimal strategy by solving the matrix Riccati equation.…”

Section: Introductionmentioning

confidence: 99%

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An Optimal Investment Strategy for Insurers in Incomplete Markets

Badaoui¹,

Fernández

Swishchuk

2018

Risks

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In this paper we consider the problem of an insurance company where the wealth of the insurer is described by a Cramér-Lundberg process. The insurer is allowed to invest in a risky asset with stochastic volatility subject to the influence of an economic factor and the remaining surplus in a bank account. The price of the risky asset and the economic factor are modeled by a system of correlated stochastic differential equations. In a finite horizon framework and assuming that the market is incomplete, we study the problem of maximizing the expected utility of terminal wealth. When the insurer's preferences are exponential, an existence and uniqueness theorem is proven for the non-linear Hamilton-Jacobi-Bellman equation (HJB). The optimal strategy and the value function have been produced in closed form. In addition and in order to show the connection between the insurer's decision and the correlation coefficient we present two numerical approaches: A Monte-Carlo method based on the stochastic representation of the solution of the insurer problem via Feynman-Kac's formula, and a mixed Finite Difference Monte-Carlo one. Finally the results are presented in the case of Scott model.

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“…In previous articles (Fernández et al 2008;Yang and Zhang 2005), the asset price was modeled by a geometric Brownian motion given by…”

Section: The Stochastic Volatility Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An Optimal Investment Strategy for Insurers in Incomplete Markets

Badaoui¹,

Fernández

Swishchuk

2018

Risks

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“…And, [44,45,52] considered optimal investment and reinsurance problems. [7,18,23,61,64,65] studied optimal investment problems for maximizing expected exponential utilities. [18,61,65] employed Black-Scholes models.…”

Section: Introductionmentioning

confidence: 99%

Expected exponential utility maximization of insurers with a Linear Gaussian stochastic factor model

Hata

Yasuda

2017

Scandinavian Actuarial Journal

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In this paper, we consider the problem of optimal investment by an insurer. The insurer invests in a market consisting of a bank account and m risky assets. The mean returns and volatilities of the risky assets depend nonlinearly on economic factors that are formulated as the solutions of general stochastic differential equations. The wealth of the insurer is described by a Cramér-Lundberg process, and the insurer preferences are exponential. Adapting a dynamic programming approach, we derive Hamilton-Jacobi-Bellman (HJB) equation. And, we prove the unique solvability of HJB equation. In addition, the optimal strategy is also obtained using the coupled forward and backward stochastic differential equations (FBSDEs). Finally, proving the verification theorem, we construct the optimal strategy.2000 Mathematics Subject Classification. 93E20, 60H30, 91B28, 91B30, 49L20, 90C40, 60J70, 62P05.

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“…Other papers using this approach justify it by relying on the conjecture that maximizing expected exponential utility is the same as or similar to minimizing the probability of ruin, see e.g. Ferguson [6], Browne [4], and Fernández et al [7].…”

Section: Introductionmentioning

confidence: 99%

Worst-Case-Optimal Dynamic Reinsurance for Large Claims

2012

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We control the surplus process of a non-life insurance company by dynamic proportional reinsurance. The objective is to maximize expected (utility of the) surplus under the worst-case claim development. In the large claim case with a worst-case upper limit on claim numbers and claim sizes, we find the optimal reinsurance strategy in a differential game setting where the insurance company plays against mother nature. We analyze the resulting strategy and illustrate its characteristics numerically. A crucial feature of our result is that the optimal strategy is robust to claim number and size modeling and robust to the choice of utility function. This robustness makes a strong case for our approach. Numerical examples illustrate the characteristics of the new approach. We analyze the optimal strategy, e.g. in terms of the more conventional, in the insurance context, objective of minimizing the probability of ruin. Finally, we calculate the intrinsic risk-free return of the model and we show that the principle of Markowitz -don't put all your eggs in one basket -does not hold in this setting.

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An optimal investment strategy with maximal risk aversion and its ruin probability

Cited by 16 publications

References 10 publications

An Optimal Investment Strategy for Insurers in Incomplete Markets

An Optimal Investment Strategy for Insurers in Incomplete Markets

Expected exponential utility maximization of insurers with a Linear Gaussian stochastic factor model

Worst-Case-Optimal Dynamic Reinsurance for Large Claims

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