Optimal dynamic risk sharing under the time‐consistent mean‐variance criterion

2021 ◽  
Vol 31 (2) ◽  
pp. 649-682
Author(s):  
Lv Chen ◽  
David Landriault ◽  
Bin Li ◽  
Danping Li
Keyword(s):  
Risk Sharing ◽  
Dynamic Risk ◽  
Optimal Dynamic ◽  
Mean Variance ◽  
Variance Criterion

scholarly journals How Risky Is That Risk Sharing Agreement? Mean-Variance Tradeoffs and Unintended Consequences of Six Common Risk Sharing Agreements

2021 ◽  
Vol 6 (1) ◽  
pp. 238146832199040
Author(s):  
Gregory S. Zaric
Keyword(s):  
Risk Sharing ◽  
Financial Risk ◽  
Unintended Consequences ◽  
Drug Costs ◽  
New Drugs ◽  
Total Drug ◽  
Number Of Patients ◽  
Clinical Benefits ◽  
The Impact ◽  
Mean Variance

Background. Pharmaceutical risk sharing agreements (RSAs) are commonly used to manage uncertainties in costs and/or clinical benefits when new drugs are added to a formulary. However, existing mathematical models of RSAs ignore the impact of RSAs on clinical and financial risk. Methods. We develop a model in which the number of patients, total drug consumption per patient, and incremental health benefits per patient are uncertain at the time of the introduction of a new drug. We use the model to evaluate the impact of six common RSAs on total drug costs and total net monetary benefit (NMB). Results. We show that, relative to not having an RSA in place, each RSA reduces expected total drug costs and increases expected total NMB. Each RSA also improves two measures of risk by reducing the probability that total drug costs exceed any threshold and reducing the probability of obtaining negative NMB. However, the effects on variance in both NMB and total drug costs are mixed. In some cases, relative to not having an RSA in place, implementing an RSA can increase variability in total drug costs or total NMB. We also show that, for some RSAs, when their parameters are adjusted so that they have the same impact on expected total drug cost, they can be rank-ordered in terms of their impact on variance in drug costs. Conclusions. Although all RSAs reduce expected total drug costs and increase expected total NMB, some RSAs may actually have the undesirable effect of increasing risk. Payers and formulary managers should be aware of these mean-variance tradeoffs and the potentially unintended results of RSAs when designing and negotiating RSAs.

Optimal Dynamic Risk-Taking

2012 ◽  
Author(s):  
Ajay Subramanian ◽  
Baozhong Yang
Keyword(s):  
Risk Taking ◽  
Dynamic Risk ◽  
Optimal Dynamic

scholarly journals A Bank Credit Model with Capital-Constrained Newsvendor Under Two Ordering Opportunities

2016 ◽  
Vol 4 (5) ◽  
pp. 408-418 ◽  
Author(s):  
Deli Zhao ◽  
Baofeng Zhang ◽  
Zongshui Wang
Keyword(s):  
Interest Rate ◽  
Capital Market ◽  
Optimal Strategies ◽  
Mathematic Model ◽  
Bank Credit ◽  
Order Quantity ◽  
Financing System ◽  
Primary Order ◽  
Mean Variance ◽  
Variance Criterion

AbstractThis paper proposes a financing system consisting of a bank under Mean-Variance criterion and a capital-constrained retailer, where the bank offers an unlimited credit to the retailer. The demand is assumed to be stochastic. The newsvendor is allowed to make an emergency order with a minimum reorder quantity threshold (RQT). It shows that under RQT, the newsvendor has different reorder strategies. The optimal primary order quantity and interest rate are derived, sequentially. Extension under perfectly competitive capital market is given. The mathematic model reveals that RQT and reorder price have significant effect on the optimal strategies.

scholarly journals Optimal Reinsurance-Investment Problem under Mean-Variance Criterion with n Risky Assets

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Peng Yang
Keyword(s):  
Financial Market ◽  
Investment Strategy ◽  
Hjb Equation ◽  
Model Parameters ◽  
Optimal Reinsurance ◽  
Risky Assets ◽  
Terminal Wealth ◽  
Investment Problem ◽  
Mean Variance ◽  
Variance Criterion

Based on the mean-variance criterion, this paper investigates the continuous-time reinsurance and investment problem. The insurer’s surplus process is assumed to follow Cramér–Lundberg model. The insurer is allowed to purchase reinsurance for reducing claim risk. The reinsurance pattern that the insurer adopts is combining proportional and excess of loss reinsurance. In addition, the insurer can invest in financial market to increase his wealth. The financial market consists of one risk-free asset and n correlated risky assets. The objective is to minimize the variance of the terminal wealth under the given expected value of the terminal wealth. By applying the principle of dynamic programming, we establish a Hamilton–Jacobi–Bellman (HJB) equation. Furthermore, we derive the explicit solutions for the optimal reinsurance-investment strategy and the corresponding efficient frontier by solving the HJB equation. Finally, numerical examples are provided to illustrate how the optimal reinsurance-investment strategy changes with model parameters.

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