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Optimal bank capital with costly recapitalization
 University of Michigan, Department of
, 2006
"... We study optimal bank capital holdings in a dynamic setting where the bank has access to external capital, but this access is subject to a fixed cost and a delay. Our model indicates that a recapitalization option may be valuable despite substantial fixed costs, and that a significant fraction of th ..."
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Cited by 20 (1 self)
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We study optimal bank capital holdings in a dynamic setting where the bank has access to external capital, but this access is subject to a fixed cost and a delay. Our model indicates that a recapitalization option may be valuable despite substantial fixed costs, and that a significant fraction of the value of low capitalized banks may be attributable to the option to recapitalize. When calibrated to data on actual bank returns, the model yields capital ratios that are significantly lower than actual bank capital ratios. This shortfall is, at least partly, explained by the skewness of the distribution of actual bank returns and by the banks ' accounting options for the provisioning of credit losses. We operate the model with implied bank return volatilities, in the same way as BlackScholes model is used in practice. Analysis of the limiting cases where the capital market imperfections vanish reveals that the capital issue delay rather than the fixed cost determines the qualitative nature of the solution.
Optimal dividends: analysis with Brownian motion
 North American Actuarial Journal
, 2004
"... In the absence of dividends, the surplus of a company is modeled by a Wiener process (or Brownian motion) with positive drift. Now dividends are paid according to a barrier strategy: whenever the (modified) surplus attains the level b, the "overflow " is paid as dividends to shareholders. An explici ..."
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Cited by 15 (1 self)
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In the absence of dividends, the surplus of a company is modeled by a Wiener process (or Brownian motion) with positive drift. Now dividends are paid according to a barrier strategy: whenever the (modified) surplus attains the level b, the "overflow " is paid as dividends to shareholders. An explicit expression for the moment generating function of the time of ruin is given. Let D denote the sum of the discounted dividends until ruin. Explicit expressions for the expectation and the moment generating function of D are given; furthermore, the limiting distribution of D is determined, when the variance parameter of the surplus process tends to infinity. It is shown that the sum of the (undiscounted) dividends until ruin is a compound geometric random variable with exponentially distributed summands. The optimal level b * is the value of b for which the expectation of D is maximal. It is shown that b * is an increasing function of the variance parameter; as the variance parameter tends to infinity, b * tends to the ratio of the drift parameter and the valuation force of interest, which can be interpreted as the present value of a perpetuity. The leverage ratio is the expectation of D divided by the initial surplus invested; it is observed that this leverage ratio is a decreasing function of the initial surplus. For b = b*, the expectation of D, considered as a function of the initial surplus, has the properties of a risk averse utility function, as long as the initial surplus is less than b*. The expected utility of D is calculated for quadratic and exponential utility functions. In an appendix, the original discrete model of De Finetti is explained and a probabilistic identity is derived. 2
Optimizing expected utility of dividend payments for a Brownian risk process and a peculiar nonlinear ODE
 Insurance Math. Econom
, 2004
"... We consider the problem of maximizing the expected utility of discounted dividend payments of an insurance company. The risk process, describing the insurance business of the company, is modeled as Brownian motion with drift. We mainly consider power utility and special emphasis is given to the limi ..."
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Cited by 4 (0 self)
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We consider the problem of maximizing the expected utility of discounted dividend payments of an insurance company. The risk process, describing the insurance business of the company, is modeled as Brownian motion with drift. We mainly consider power utility and special emphasis is given to the limiting behavior when the coefficient of risk aversion tends to zero. We then find convergence of the corresponding dividend strategies to the classical case of maximizing the expected dividend payments.
APPROXIMATION OF OPTIMAL REINSURANCE AND DIVIDEND PAYOUT POLICIES
"... We consider the stochastic process of the liquid assets of an insurance company assuming that the management can control this process in two ways: first, the risk exposure can be reduced by effecting reinsurance which decreases the premium income. Second, a dividend has to be paid out to the shareho ..."
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We consider the stochastic process of the liquid assets of an insurance company assuming that the management can control this process in two ways: first, the risk exposure can be reduced by effecting reinsurance which decreases the premium income. Second, a dividend has to be paid out to the shareholders. The aim is to maximize the expected discounted dividend payout until the time of bankruptcy. The classical approach is to model the liquid assets or risk reserve process of the company as a piecewise deterministic Markov process. However, within this setting the control problem is very hard. Recently several papers have modeled this problem as a controlled diffusion, presuming that the obtained policy is in some sense good for the piecewise deterministic problem as well. We will clarify this statement in our paper. More precisely, we will first show that the value function of the controlled diffusion provides an asymptotic upper bound for the value functions of the piecewise deterministic problems under diffusion scaling. Finally it can be shown that the upper bound is achieved in the limit under the optimal feedback control of the diffusion problem. This property is called asymptotic optimality. Key Words: dividend payout, proportional reinsurance, piecewise deterministic process, diffusion process, asymptotic optimality, HamiltonJacobiBellman equation 0 The author would like to thank Paul Embrechts for a fruitful discussion and two referees for valuable comments. 1
Developments in Insurance Mathematics
"... Insurance mathematics in the 1990s has been influenced firstly, by the increase in catastrophic claims which had already become apparent during the early 1970s and 1980s and required new mathematical and statistical methods, and, secondly, by a fast increasing financial market that is interested in ..."
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Insurance mathematics in the 1990s has been influenced firstly, by the increase in catastrophic claims which had already become apparent during the early 1970s and 1980s and required new mathematical and statistical methods, and, secondly, by a fast increasing financial market that is interested in new investment possibilities. Ideas from extremevalue theory and mathematical finance have been introduced into insurance mathematics and enriched classical insurance methods. But the exchange is not only from mathematical finance to insurance mathematics. The continuing occurrence of crashes in the financial market has led to a new development in mathematical finance: models and tools from insurance mathematics have entered the world of finance. This paper presents examples, from both the insurance and the financial worlds. The choice of topics is guided by personal taste and my own work.
Entrenchment: A ContinuousTime Stochastic ControlTheoretic Model ∗
"... In this paper, we formulate a model prescribing optimal policy for cash disbursements and seasoned equity offerings taking into account the principalagent problems inherent in these decisions. In order to discipline managers, stockholders demand that excess free cash flow be disbursed either as cas ..."
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In this paper, we formulate a model prescribing optimal policy for cash disbursements and seasoned equity offerings taking into account the principalagent problems inherent in these decisions. In order to discipline managers, stockholders demand that excess free cash flow be disbursed either as cash dividends or through stock repurchases. Managers resist stockholders in this regard since they prefer to retain excess free cash flow in order to pursue personal interests and reduce the probability that the company will experience financial distress in the future. However, as a consequence of withholding cash disbursements, managers incur disutility due to the possibility that their control of the firm could be threatened by the market for corporate control. We model this situation as a stochastic impulse control problem, and succeed in finding an analytical solution. We derive several testable implications, some of which have not been fully addressed in the corporate finance literature.
Bank of Finland Discussion Papers 4/2003
, 2003
"... Simulationbased stress testing of banks ’ regulatory capital adequacy Suomen Pankin keskustelualoitteita ..."
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Simulationbased stress testing of banks ’ regulatory capital adequacy Suomen Pankin keskustelualoitteita
INTERPLAY BETWEEN DIVIDEND RATE AND BUSINESS CONSTRAINTS FOR A FINANCIAL CORPORATION
, 2005
"... We study a model of a corporation which has the possibility to choose various production/business policies with different expected profits and risks. In the model there are restrictions on the dividend distribution rates as well as restrictions on the risk the company can undertake. The objective is ..."
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We study a model of a corporation which has the possibility to choose various production/business policies with different expected profits and risks. In the model there are restrictions on the dividend distribution rates as well as restrictions on the risk the company can undertake. The objective is to maximize the expected present value of the total dividend distributions. We outline the corresponding Hamilton–Jacobi–Bellman equation, compute explicitly the optimal return function and determine the optimal policy. As a consequence of these results, the way the dividend rate and business constraints affect the optimal policy is revealed. In particular, we show that under certain relationships between the constraints and the exogenous parameters of the random processes that govern the returns, some business activities might be redundant, that is, under the optimal policy they will never be used in any scenario. 1. Introduction. In
Optimal Reinsurance Strategy under Fixed Cost and Delay
"... We consider an optimal reinsurance strategy in which the insurance company (1) monitors the dynamics of its surplus process, (2) optimally chooses a time to begin negotiating with a reinsurer to buy quotashare, or proportional, reinsurance, which introduces an implementation delay (denoted by ∆ ≥ ..."
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We consider an optimal reinsurance strategy in which the insurance company (1) monitors the dynamics of its surplus process, (2) optimally chooses a time to begin negotiating with a reinsurer to buy quotashare, or proportional, reinsurance, which introduces an implementation delay (denoted by ∆ ≥ 0), (3) chooses the optimal proportion at the beginning of the negotiation period, and (4) pays a fixed transaction cost when the contract is signed ( ∆ units of time after negotiation begins). This setup leads to a combined problem of optimal stopping and stochastic control. We obtain a solution for the value function and the corresponding optimal strategy, while demonstrating the solution procedure in detail. It turns out that the optimal continuation region is a union of two intervals, a rather rare occurrence in optimal stopping. Numerical examples are given to illustrate our results and we discuss relevant economic insights from this model.