Optimal Consumption and Investment for a Large Investor: An Intensity‐based Control Framework

Busch, Michael T.; Korn, Ralf; Seifried, Frank Thomas

doi:10.1111/j.1467-9965.2012.00528.x

Cited by 13 publications

(9 citation statements)

References 17 publications

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“…As parameter κ k captures the degree of dependence on the terminal wealth of insurer k's competitor (see Problem 3.1), a higher κ k results in insurer k becoming more concerned with his performance compared with that of his competitor in the terminal period T . While purchasing proportional reinsurance can reduce the risk borne by insurer k, it is nonetheless costly because insurer k needs to pay (1 − a * k (0))θ k to the reinsurance company for the reinsurance protection (see (6)), which decreases his terminal wealth value relative to that of his competitor, X k (T ) − κ k X m (T ), for k = m ∈ {1, 2}. In the case when the correlation between the insurance companies is positive, i.e.…”

Section: Numerical Illustrationsmentioning

confidence: 99%

A class of non-zero-sum stochastic differential investment and reinsurance games

et al. 2014

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In this article, we provide a systematic study on the nonzero-sum stochastic differential investment and reinsurance game between two insurance companies. Each insurance company's surplus process consists of a proportional reinsurance protection and an investment in risky and risk-free assets. Each insurance company is assumed to maximize his utility of the difference between his terminal surplus and that of his competitor. The surplus process of each insurance company is modeled by a mixed regime-switching Cramer-Lundberg diffusion approximation process, i.e. the coefficients of the diffusion risk processes are modulated by a continuous-time Markov chain and an independent market-index process. Correlation between the two surplus processes, independent of the risky asset process, is allowed. Despite the complex structure, we manage to solve the resulting non-zero sum game problem by applying the dynamic programming principle. The Nash equilibrium, the optimal reinsurance/investment, and the resulting value processes of the insurance companies are obtained in closed forms, together with sound economic interpretations, for the case of an exponential utility function.

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Section: Numerical Illustrationsmentioning

confidence: 99%

A class of non-zero-sum stochastic differential investment and reinsurance games

et al. 2014

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“…In principle, one can solve the system numerically using, for instance, backward Euler method. In particular, as pointed out in [10], at each time step t n of the numerical procedure one should find the maximizer h * (t n ), and then solve the resulting ODE.…”

Section: Logarithmic Utility -Market Impactmentioning

confidence: 99%

“…There is ample amount of literature related to the optimal decision of a large investor, analyzed in various settings. The most related work to ours is [10] that studies the optimal consumption-portfolio choice problem, in which the asset price dynamics are given by a jump-diffusion affected by the regime-switching environment controlled by a large investor in a full information setting. They show that optimal strategies have significant deviations from the strategies obtained in the classical Merton problem.…”

Section: Introductionmentioning

confidence: 99%

Portfolio Optimization for a Large Investor Controlling Market Sentiment Under Partial Information

Altay¹,

Colaneri²,

Eksi³

2019

SIAM J. Finan. Math.

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We consider an investor faced with the utility maximization problem in which the risky asset price process has pure-jump dynamics affected by an unobservable continuous-time finite-state Markov chain, the intensity of which can also be controlled by actions of the investor. Using the classical filtering theory, we reduce this problem with partial information to one with full information and solve it for logarithmic and power utility functions. In particular, we apply control theory for piecewise deterministic Markov processes (PDMP) to our problem and derive the optimality equation for the value function and characterize the value function as the unique viscosity solution of the associated dynamic programming equation. Finally, we provide a toy example, where the unobservable state process is driven by a two-state Markov chain, and discuss how investor's ability to control the intensity of the state process affects the optimal portfolio strategies as well as the optimal wealth under both partial and full information cases.

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“… First, the current model can be generalized to accommodate different types of managerial flexibility to minimize the potential myopic decisions arising from the ignorance of potential sources of managerial flexibility. Second, it would be interesting to examine the case where the intensities of switching from one market mode to the other are affected by other factors. For example, Busch, Korn, and Seifried () developed a large investor model to study the investor's consumption and investment decision where the regime switching intensities depend on the investor's decision. Elliott, Siu, and Badescu () studied the pricing and hedging of European options where the asset price dynamics has a feedback effect on the jump rate.…”

Section: Further Remarksmentioning

confidence: 99%

Real Options With Competition and Regime Switching

Bensoussan

Hoe

Zhang

et al. 2014

Mathematical Finance

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In this paper, we examine irreversible investment decisions in duopoly games with a variable economic climate. Integrating timing flexibility, competition, and changes in the economic environment in the form of a cash flow process with regime switching, the problem is formulated as a stopping-time game under Stackelberg leader-follower competition, in which both players determine their respective optimal market entry time. By extending the variational inequality approach, we solve for the free boundaries and obtain optimal investment strategies for each player. Despite the lack of regularity in the leader's obstacle and the cash flow regime uncertainty, the regime-dependent optimal policies for both the leader and the follower are obtained. In addition, we perform comprehensive numerical experiments to demonstrate the properties of solutions and to gain insights into the implications of regime switching.

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Optimal Consumption and Investment for a Large Investor: An Intensity‐based Control Framework

Cited by 13 publications

References 17 publications

A class of non-zero-sum stochastic differential investment and reinsurance games

A class of non-zero-sum stochastic differential investment and reinsurance games

Portfolio Optimization for a Large Investor Controlling Market Sentiment Under Partial Information

Real Options With Competition and Regime Switching

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