Optimal investment to minimize the probability of drawdown

Angoshtari, Bahman; Bayraktar, Erhan; Young, Virginia R.

doi:10.1080/17442508.2016.1155590

Cited by 24 publications

(25 citation statements)

References 21 publications

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“…Furthermore, in combination with Proposition 1, we can see that either drawdown occurs with probability (u, m) = P( < ∞) or the optimal controlled surplus value lies strictly between m and u s , for all time, with probability of 1 − (u, m). The similar conclusion is also derived in the works of Bayraktar and Zhang, 23 Angoshtari et al, 5 and Han et al 6,7…”

Section: Reaching the Safe Levelsupporting

confidence: 87%

“…Note that when = 0, minimizing the probability of drawdown is equal to minimizing the probability of ruin. Angoshtari et al 5 and Han et al 6,7 minimized the probability of drawdown over an infinite-time horizon and showed that the strategy which minimizes the probability of ruin also minimizes the probability of drawdown. Besides, Angoshtari et al 8 and Chen et al 9 computed the optimal investment strategy to minimize the probability of lifetime drawdown for an individual investor.…”

Section: Introductionmentioning

confidence: 99%

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Optimal reinsurance and investment in danger‐zone and safe‐region

Han

Liang

2020

Optim Control Appl Methods

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This paper studies the optimal reinsurance-investment problems for an insurance company where the claim process follows a Brownian motion with drift. It turns out that there is a region where the probability of drawdown, namely, the probability that the value of the insurer's surplus process reaches some fixed fractional value of its maximum value to date is positive. Then in the complementary region, drawdown can be avoided with certainty. For this reason, we call the former region the "danger-zone" and "safe-region" for the latter. In the danger-zone, we consider the problem of minimizing the probability of drawdown; and in the safe-region, we turn our attention to the optimization problem of minimizing the expected time to reach a given capital level. Using the technique of stochastic control theory and the corresponding Hamilton-Jacobi-Bellman equation, explicit expressions of the optimal reinsurance-investment strategies and the associated value functions are derived for the two optimization problems. Moreover, we provide several detailed comparisons to investigate the impact of some important parameters on the optimal strategies and illustrate the observation from behavior finance of view. K E Y W O R D Sdiffusion approximation model, Hamilton-Jacobi-Bellman equation, investment, proportional reinsurance, stochastic optimal control

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Section: Reaching the Safe Levelsupporting

confidence: 87%

Section: Introductionmentioning

confidence: 99%

Optimal reinsurance and investment in danger‐zone and safe‐region

Han

Liang

2020

Optim Control Appl Methods

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“…Under this reinsurance strategy, the value of the surplus process is non-decreasing, so drawdown will never occur. For this reason, we call u s safe level as defined in Angoshtari et al (2016a).…”

Section: Model and Problem Formulationmentioning

confidence: 99%

“…In the second case, the level is not necessarily a fixed one, then the method mentioned above does not apply. Thus, following the analysis of Chen et al (2015) and Angoshtari et al (2016aAngoshtari et al ( , 2016b, we use the technique of stochastic control theory and the corresponding HJB equation to tackle the optimisation problem. In particular, since we constrain the reinsurance proportion in the interval [0,1] for each case, the optimisation problems are discussed in three different situations, which makes the problem more challenging.…”

Section: Introductionmentioning

confidence: 99%

Optimal proportional reinsurance with common shock dependence to minimise the probability of drawdown

2018

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In this paper, we study the optimal proportional reinsurance problem in a risk model with two dependent classes of insurance business, where the two claim number processes are correlated through a common shock component, and the criterion is to minimise the probability of drawdown, namely, the probability that the value of the surplus process reaches some fixed proportion of its maximum value to date. By the method of maximising the ratio of drift of a diffusion divided to its volatility squared, and the technique of stochastic control theory and the corresponding Hamilton–Jacobi–Bellman equation, we investigate the optimisation problem in two different cases. Furthermore, we constrain the reinsurance proportion in the interval [0,1] for each case, and derive the explicit expressions of the optimal proportional reinsurance strategy and the minimum probability of drawdown. Finally, some numerical examples are presented to show the impact of model parameters on the optimal results.

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“…We point out that a recent paper by Angoshtari et al (2015b) also studied the minimum drawdown probability problem but over an infinite-time horizon. By utilizing the results of Bäuerle and Bayraktar (2014), the authors found that the minimum infinitetime drawdown probability (MIDP) strategy coincides with the minimum infinite-time ruin probability (MIRP) strategy which consists in maximizing the ratio of the drift of the value process to its volatility squared.…”

Section: Introductionmentioning

confidence: 97%