Minimizing the Probability of Ruin When Claims Follow Brownian Motion with Drift

Promislow, S. David; Young, Virginia R.

doi:10.1080/10920277.2005.10596214

Cited by 192 publications

(120 citation statements)

References 9 publications

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“…These figures are comparable to the parameter set given in Liu & Yang (2004) and Promislow & Young (2005) for a compound Poisson risk process and exponential claims using a normal approximation (see (31)). We vary µ which in effect varies the dimensionless risk parameter η and plot the results in Figure 1.…”

Section: Normal Risk Processsupporting

confidence: 62%

Asymptotic and numerical analysis of the optimal investment strategy for an insurer

Emms

Haberman

2007

Insurance: Mathematics and Economics

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The asymptotic behaviour of the optimal investment strategy for an insurer is analysed for a number of cash flow processes. The insurer's portfolio consists of a risky stock and a bond and the cash flow is assumed to be either a normal or a compound Poisson process. For a normally distributed cash flow, the asymptotic limits are found in the cases that the stock is very risky or very safe. For a compound Poisson risk process, a composite asymptotic expansion is found for the optimal investment strategy in the case that stock is very risky and the claim size distribution is of an exponential type.In general for a compound Poisson cash flow, the outer asymptotic limit reduces the integro-differential equation describing the optimal stock allocation to an integral equation, which determines the classical survival probability in ruin theory. The leading order optimal asset allocation is derived from this survival probability through a feedback law. Calculation of the optimal asset allocation leads to a difficult numerical problem because of the boundary layer structure of the solution and the tail properties of the claim size distribution. A second order numerical method is successfully developed to calculate the optimal allocation for light and heavy-tailed claim size distributions.

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Section: Normal Risk Processsupporting

confidence: 62%

Asymptotic and numerical analysis of the optimal investment strategy for an insurer

Emms

Haberman

2007

Insurance: Mathematics and Economics

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“…See, for example, Milevsky, Ho, and Robinson (1997), Milevsky and Robinson (2000), and Young (2004). In insurance mathematics, the criteria of minimizing the probability of ruin was used to find the optimal reinsurance; see, for example, Schmidli 2001, Taksar andMarkussen (2003), and Promislow and Young (2005). Young (2004) studied the problem of finding the investment strategy to minimize the probability of lifetime ruin.…”

Section: For Details)mentioning

confidence: 99%

Minimizing the lifetime shortfall or shortfall at death

Bayraktar

Young

2009

Insurance: Mathematics and Economics

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We find the optimal investment strategy for an individual who seeks to minimize one of four objectives: (1) the probability that his wealth reaches a specified ruin level before death, (2) the probability that his wealth reaches that level at death, (3) the expectation of how low his wealth drops below a specified level before death, and (4) the expectation of how low his wealth drops below a specified level at death. Young (2004) showed that under criterion (1), the optimal investment strategy is a heavily leveraged position in the risky asset for low wealth.In this paper, we introduce the other three criteria in order to reduce the leveraging observed by Young (2004). We discovered that surprisingly the optimal investment strategy for criterion (3) is identical to the one for (1) and that the strategies for (2) and (4) are more leveraged than the one for (1) at low wealth. Because these criteria do not reduce leveraging, we completely remove it by considering problems (1) and (3) under the restriction that the individual cannot borrow to invest in the risky asset.

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“…To achieve this goal, there has been much attention in the literature in security market and/or reinsurance-related products [1][2][3][4][5][6][7][8][9]. The insurer is tempted to put his/her surplus into the risky investment so as to obtain a higher potential return.…”

Section: Introductionmentioning

confidence: 99%

Optimal Investment and Proportional Reinsurance with Risk Constraint

Liu¹,

Yiu²,

Loxton³

et al. 2013

JMF

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In this paper, we investigate the problem of maximizing the expected exponential utility for an insurer. In the problem setting, the insurer can invest his/her wealth into the market and he/she can also purchase the proportional reinsurance. To control the risk exposure, we impose a value-at-risk constraint on the portfolio, which results in a constrained stochastic optimal control problem. It is difficult to solve a constrained stochastic optimal control problem by using traditional dynamic programming or Martingale approach. However, for the frequently used exponential utility function, we show that the problem can be simplified significantly using a decomposition approach. The problem is reduced to a deterministic constrained optimal control problem, and then to a finite dimensional optimization problem. To show the effectiveness of the approach proposed, we consider both complete and incomplete markets; the latter arises when the number of risky assets are fewer than the dimension of uncertainty. We also conduct numerical experiments to demonstrate the effect of the risk constraint on the optimal strategy.

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Minimizing the Probability of Ruin When Claims Follow Brownian Motion with Drift

Cited by 192 publications

References 9 publications

Asymptotic and numerical analysis of the optimal investment strategy for an insurer

Asymptotic and numerical analysis of the optimal investment strategy for an insurer

Minimizing the lifetime shortfall or shortfall at death

Optimal Investment and Proportional Reinsurance with Risk Constraint

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