scholarly journals Optimal Dividend and Capital Injection Problem with Transaction Cost and Salvage Value: The Case of Excess-of-Loss Reinsurance Based on the Symmetry of Risk Information

Symmetry ◽  
2018 ◽  
Vol 10 (7) ◽  
pp. 276 ◽  
Author(s):  
Qingyou Yan ◽  
Le Yang ◽  
Tomas Baležentis ◽  
Dalia Streimikiene ◽  
Chao Qin
Keyword(s):  
Transaction Cost ◽  
Risk Information ◽  
Insurance Company ◽  
Optimal Control Strategy ◽  
Ruin Time ◽  
Discounted Cost ◽  
Capital Injection ◽  
Surplus Process ◽  
Optimal Dividend ◽  
A Company

This paper considers the optimal dividend and capital injection problem for an insurance company, which controls the risk exposure by both the excess-of-loss reinsurance and capital injection based on the symmetry of risk information. Besides the proportional transaction cost, we also incorporate the fixed transaction cost incurred by capital injection and the salvage value of a company at the ruin time in order to make the surplus process more realistic. The main goal is to maximize the expected sum of the discounted salvage value and the discounted cumulative dividends except for the discounted cost of capital injection until the ruin time. By considering whether there is capital injection in the surplus process, we construct two instances of suboptimal models and then solve for the corresponding solution in each model. Lastly, we consider the optimal control strategy for the general model without any restriction on the capital injection or the surplus process.

scholarly journals REFRACTION–REFLECTION STRATEGIES IN THE DUAL MODEL

2016 ◽  
Vol 47 (1) ◽  
pp. 199-238 ◽  
Author(s):  
José-Luis Pérez ◽  
Kazutoshi Yamazaki
Keyword(s):  
Additional Condition ◽  
Numerical Results ◽  
Dual Model ◽  
Maximal Rate ◽  
Absolutely Continuous ◽  
Capital Injection ◽  
Surplus Process ◽  
Optimal Dividend

AbstractWe study the dual model with capital injection under the additional condition that the dividend strategy is absolutely continuous. We consider a refraction–reflection strategy that pays dividends at the maximal rate whenever the surplus is above a certain threshold, while capital is injected so that it stays non-negative. The resulting controlled surplus process becomes the spectrally positive version of the refracted–reflected process recently studied by Pérez and Yamazaki (2015). We study various fluctuation identities of this process and prove the optimality of the refraction–reflection strategy. Numerical results on the optimal dividend problem are also given.

scholarly journals Optimal dividends and capital injection under dividend restrictions

2020 ◽  
Vol 92 (3) ◽  
pp. 461-487 ◽  
Author(s):  
Kristoffer Lindensjö ◽  
Filip Lindskog
Keyword(s):  
Optimal Strategy ◽  
Stopping Time ◽  
Type I ◽  
Insurance Company ◽  
Type Ii ◽  
Dividend Payout ◽  
Optimal Dividends ◽  
Capital Injection ◽  
Surplus Process ◽  
Dividend Payments

AbstractWe study a singular stochastic control problem faced by the owner of an insurance company that dynamically pays dividends and raises capital in the presence of the restriction that the surplus process must be above a given dividend payout barrier in order for dividend payments to be allowed. Bankruptcy occurs if the surplus process becomes negative and there are proportional costs for capital injection. We show that one of the following strategies is optimal: (i) Pay dividends and inject capital in order to reflect the surplus process at an upper barrier and at 0, implying bankruptcy never occurs. (ii) Pay dividends in order to reflect the surplus process at an upper barrier and never inject capital—corresponding to absorption at 0—implying bankruptcy occurs the first time the surplus reaches zero. We show that if the costs of capital injection are low, then a sufficiently high dividend payout barrier will change the optimal strategy from type (i) (without bankruptcy) to type (ii) (with bankruptcy). Moreover, if the costs are high, then the optimal strategy is of type (ii) regardless of the dividend payout barrier. We also consider the possibility for the owner to choose a stopping time at which the insurance company is liquidated and the owner obtains a liquidation value. The uncontrolled surplus process is a Wiener process with drift.

scholarly journals Minimizing spectral risk measures applied to Markov decision processes

2021 ◽  
Author(s):  
Nicole Bäuerle ◽  
Alexander Glauner
Keyword(s):  
Minimization Problem ◽  
Risk Measures ◽  
Risk Measure ◽  
Sufficient Conditions ◽  
Planning Horizon ◽  
Insurance Company ◽  
Existence Of A Solution ◽  
Discounted Cost ◽  
Spectral Risk Measures ◽  
Markov Decision

AbstractWe study the minimization of a spectral risk measure of the total discounted cost generated by a Markov Decision Process (MDP) over a finite or infinite planning horizon. The MDP is assumed to have Borel state and action spaces and the cost function may be unbounded above. The optimization problem is split into two minimization problems using an infimum representation for spectral risk measures. We show that the inner minimization problem can be solved as an ordinary MDP on an extended state space and give sufficient conditions under which an optimal policy exists. Regarding the infinite dimensional outer minimization problem, we prove the existence of a solution and derive an algorithm for its numerical approximation. Our results include the findings in Bäuerle and Ott (Math Methods Oper Res 74(3):361–379, 2011) in the special case that the risk measure is Expected Shortfall. As an application, we present a dynamic extension of the classical static optimal reinsurance problem, where an insurance company minimizes its cost of capital.

scholarly journals ON THE OPTIMAL DIVIDEND PROBLEM FOR A SPECTRALLY POSITIVE LÉVY PROCESS

2014 ◽  
Vol 44 (3) ◽  
pp. 635-651 ◽  
Author(s):  
Chuancun Yin ◽  
Yuzhen Wen ◽  
Yongxia Zhao
Keyword(s):  
Lévy Process ◽  
Risk Model ◽  
Levy Process ◽  
Dual Model ◽  
Threshold Strategy ◽  
Classical Risk Model ◽  
Surplus Process ◽  
Optimal Dividend ◽  
Special Cases ◽  
The Classical Risk Model

AbstractIn this paper we study the optimal dividend problem for a company whose surplus process evolves as a spectrally positive Lévy process before dividends are deducted. This model includes the dual model of the classical risk model and the dual model with diffusion as special cases. We assume that dividends are paid to the shareholders according to an admissible strategy whose dividend rate is bounded by a constant. The objective is to find a dividend policy so as to maximize the expected discounted value of dividends which are paid to the shareholders until the company is ruined. We show that the optimal dividend strategy is formed by a threshold strategy.

scholarly journals Dividend maximization in a hidden Markov switching model

2015 ◽  
Vol 32 (3-4) ◽  
pp. 143-158
Author(s):  
Michaela Szölgyenyi
Keyword(s):  
Markov Chain ◽  
Partial Information ◽  
Numerical Study ◽  
Insurance Company ◽  
Markov Switching Model ◽  
Switching Model ◽  
Surplus Process ◽  
Dividend Payments ◽  
Current State ◽  
Optimal Value

Abstract In this paper we study the valuation problem of an insurance company by maximizing the expected discounted future dividend payments in a model with partial information that allows for a changing economic environment. The surplus process is modeled as a Brownian motion with drift. This drift depends on an underlying Markov chain the current state of which is assumed to be unobservable. The different states of the Markov chain thereby represent different phases of the economy. We apply results from filtering theory to overcome uncertainty and then we give an analytic characterization of the optimal value function. Finally, we present a numerical study covering various scenarios to get a clear picture of how dividends should be paid out.

Developing Risk Skills: An Investigation of Business Risks and Controls at Prudential Insurance Company of America

2001 ◽  
Vol 16 (2) ◽  
pp. 291-313 ◽  
Author(s):  
Paul L. Walker ◽  
William G. Shenkir ◽  
C. Stephen Hunn
Keyword(s):  
Risk Assessment ◽  
Corporate Culture ◽  
Life Insurance ◽  
Control Environment ◽  
Insurance Company ◽  
Special Committee ◽  
Business Professionals ◽  
Poor Control ◽  
Assurance Services ◽  
A Company

The Prudential Insurance Company was involved in the largest life insurance churning scam of the 1980s and early 1990s. At the time, Prudential had weak business controls, and its corporate culture was characterized as ineffective and loose. However, this scandal is rooted in something deeper than a poor control environment. Prudential was a company facing several risks; many company decisions allowed these risks to have a dramatic impact on the company. As a result, its weak control environment came to the forefront, allowing the churning scam to reach its record levels. This case demonstrates the value of identifying and assessing risks in an organization. Further, the case demonstrates how to build control solutions to match the risks. Learning how to manage risks is a valuable skill for business professionals. In fact, the AICPA's Special Committee on Assurance Services (AICPA 1997), also known as the Elliott Committee, identified risk assessment as one of the emerging assurance services offered by CPAs.

Life

2020 ◽  
pp. 8-32
Author(s):  
Benjamin Wiggins
Keyword(s):  
Public Relations ◽  
Insurance Industry ◽  
Theoretical Work ◽  
Business Practices ◽  
Insurance Company ◽  
Company Policy ◽  
History Of ◽  
A Company ◽  
History Of Race

Chapter 1 focuses on the early history of race-based insurance. When the Newark-based Prudential Insurance Company of America incorporated in 1875, it revolutionized the American insurance industry by offering policies to the working class for an affordable three cents per week. What made the Prudential doubly unique was that the company insured not simply industrial laborers, but also African American laborers. The company was not in the progressive vanguard, though. Rather, the Northern upstart, in contrast to its Southern competitors, simply had not thought to craft a company policy to explicitly ban African Americans from purchasing life insurance. Just five years after becoming the first insurer to cover black lives, the Prudential began to charge differential, race-based premiums and commenced a public relations effort to defend its discriminatory practices. This foundational chapter traces how the theoretical work of scientific racism became embedded in the business practices of American insurers.

scholarly journals Optimal loss-carry-forward taxation for Lévy risk processes stopped at general draw-down time

2019 ◽  
Vol 51 (03) ◽  
pp. 865-897 ◽  
Author(s):  
Wenyuan Wang ◽  
Zhimin Zhang
Keyword(s):  
Objective Function ◽  
Insurance Company ◽  
Tax System ◽  
Ruin Time ◽  
Return Function ◽  
Numerical Examples ◽  
Optimal Tax ◽  
Spectrally Negative Lévy Process ◽  
Tax Payments ◽  
Risk Processes

AbstractMotivated by Avram, Vu and Zhou (2017), Kyprianou and Zhou (2009), Li, Vu and Zhou (2017), Wang and Hu (2012), and Wang and Zhou (2018), we consider in this paper the problem of maximizing the expected accumulated discounted tax payments of an insurance company, whose reserve process (before taxes are deducted) evolves as a spectrally negative Lévy process with the usual exclusion of negative subordinator or deterministic drift. Tax payments are collected according to the very general loss-carry-forward tax system introduced in Kyprianou and Zhou (2009). To achieve a balance between taxation optimization and solvency, we consider an interesting modified objective function by considering the expected accumulated discounted tax payments of the company until the general draw-down time, instead of until the classical ruin time. The optimal tax return function and the optimal tax strategy are derived, and some numerical examples are also provided.

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