Nonconcave Optimal Investment with Value-at-Risk Constraint: An Application to Life Insurance Contracts

Nguyen, Thai; Stadje, Mitja

doi:10.1137/18m1217322

Cited by 27 publications

(4 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The insurer has to fulfill a Value-at-Risk (VaR) constraint, which is widely used in the life insurance literature (see e.g., Dong and Zheng (2020), Guan and Liang (2016), Nguyen and Stadje (2020)) and is motivated by solvency regulations and the management rules of insurance companies. We denote by ε ∈ [0, 1] the probability of not achieving a guarantee by the insurer.…”

Section: Problem Settingmentioning

confidence: 99%

Decrease of capital guarantees in life insurance products: can reinsurance stop it?

Escobar‐Anel¹,

Havrylenko²,

Kschonnek³

et al. 2021

Preprint

View full text Add to dashboard Cite

We analyze the potential of reinsurance for reversing the current trend of decreasing capital guarantees in life insurance products. Providing an insurer with an opportunity to shift part of the financial risk to a reinsurer, we solve the insurer's dynamic investment-reinsurance optimization problem under simultaneous Value-at-Risk and no-short-selling constraints. We introduce the concept of guarantee-equivalent utility gain and use it to compare life insurance products with and without reinsurance. Our numerical studies indicate that the optimally managed reinsurance allows the insurer to offer significantly higher capital guarantees to clients without any loss in the insurer's expected utility. The longer the investment horizon and the less risk-averse the insurer, the more prominent the reinsurance benefit.

show abstract

Section: Problem Settingmentioning

confidence: 99%

Decrease of capital guarantees in life insurance products: can reinsurance stop it?

Escobar‐Anel¹,

Havrylenko²,

Kschonnek³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Risk management (RM) under downside constraints has been widely considered in the literature, see, for example, Grossman and Vila (1989); Basak (1995); Grossman and Zhou (1996); Jensen and Sørensen (2001); Gabih et al (2009); Chen et al (2018); ; Dong and Zheng (2020); Nguyen and Stadje (2020); Escobar-Anel et al (2021); Gu et al (2021). The LERL-RM framework is suggested by Basak et al (2006), where only the optimal terminal wealth for the stock market benchmark is given without rigorous proof.…”

Section: Introductionmentioning

confidence: 99%

Portfolio performance under benchmarking relative loss and portfolio insurance: From omega ratio to loss aversion

Nguyen²

2023

ASTIN Bull.

Self Cite

View full text Add to dashboard Cite

We study an optimal investment problem under a joint limited expected relative loss and portfolio insurance constraint with a general random benchmark. By making use of a static Lagrangian method in a complete market setting, the optimal wealth and investment strategy can be fully determined along with the existence and uniqueness of the Lagrangian multipliers. Our numerical demonstration for various commonly used random benchmarks shows a trade-off between the portfolio outperformance and underperformance relative to the benchmark, which may not be captured by the widely used Omega ratio and its utility-transformed version, reflecting the impact of the benchmarking loss constraint. Furthermore, we develop a new portfolio performance measurement indicator that incorporates the agent’s utility loss aversion relative to the benchmark via solving an equivalent optimal asset allocation problem with a benchmark-reference-based preference. We show that the expected utility performance is well depicted by looking at this new portfolio performance ratio, suggesting a more suitable portfolio performance measurement under a limited loss constraint relative to a possibly random benchmark.

show abstract

“…Financial companies make decisions about how to control their risk exposure optimally through business activities aimed at maximizing or minimizing various objective functions. Such decisions have recently been the focus of numerous studies (e.g., Choulli et al (2003), He et al (2015), Nguyen and Stadje (2020)). In particular, the literature (Cuoco et al (2008) and Nguyen and Stadje (2020)) has considered the risk-taking restrictions that commonly occur in the business activities opportunity set due to institutional or regulatory reasons.…”

Section: Introductionmentioning

confidence: 99%

Optimal Expansion of Business Opportunity

Chen¹,

Chiu²,

Wong³

2021

Preprint

View full text Add to dashboard Cite

Any firm whose business strategy has an exposure constraint that limits its potential gain naturally considers expansion, as this can increase its exposure. We model business expansion as an enlargement of the opportunity set for business policies. However, expansion is irreversible and has an opportunity cost attached. We use the expected optimization of utility to formulate this as a novel stochastic control problem combined with an optimal stopping time, and we derive an explicit solution for exponential utility.We apply the framework to an investment and a reinsurance scenario. In the investment problem, the cost and incentives to increase the trading exposure are analyzed, while the optimal timing for an insurer to launch its reinsurance business is investigated in the reinsurance problem. Our model predicts that the additional income gained through business expansion is the key incentive for a decision to expand. Interestingly, companies may have this incentive but are likely to wait for a period of time before expanding, although situations of zero opportunity cost or specific restrictive conditions on the model parameters are exceptions to waiting. The business policy remains on the boundary of the opportunity set before expansion during the waiting period. The length of the waiting period is related to the opportunity cost, return, and risk of the expanded business.

show abstract

Nonconcave Optimal Investment with Value-at-Risk Constraint: An Application to Life Insurance Contracts

Cited by 27 publications

References 40 publications

Decrease of capital guarantees in life insurance products: can reinsurance stop it?

Decrease of capital guarantees in life insurance products: can reinsurance stop it?

Portfolio performance under benchmarking relative loss and portfolio insurance: From omega ratio to loss aversion

Optimal Expansion of Business Opportunity

Contact Info

Product

Resources

About