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19
Optimal partially reversible investment with entry decision and general production function
, 2005
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A mixed singular/switching control problem for a dividend policy with reversible . . .
, 2006
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On optimal harvesting problems in random environments
 SIAM J. Control Optim
, 2011
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From Basel I to Basel II: an analysis of the three pillars. CEMFI Working Paper No. 0704
, 2007
"... This paper presents a dynamic model of banking supervision to analyze the impact of each of Basel II three pillars on banks ’ risk taking. We extend previous literature providing an analysis of ratingsbased supervisory policies. In Pillar 2 (supervisory review) the supervisor audits more frequentl ..."
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This paper presents a dynamic model of banking supervision to analyze the impact of each of Basel II three pillars on banks ’ risk taking. We extend previous literature providing an analysis of ratingsbased supervisory policies. In Pillar 2 (supervisory review) the supervisor audits more frequently low rated banks and restricts their dividend payments in order to build capital. In Pillar 3 (market discipline) the supervisor reduces the level of deposit insurance coverage compelling notfully insured depositors to adjust interest rates contingent on the bank’s external rating. We also analyze the risk sensitiveness of Pillar 1 (capital requirements) concluding that all three Pillars reduce banks’ risk taking incentives.
Finite time dividendruin models
"... We consider the finite time horizon dividendruin model where the firm pays out dividends to its shareholders according to a dividendbarrier strategy and becomes ruined when the firm asset value falls below the default threshold. The asset value process is modeled as a restricted Geometric Brownian ..."
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We consider the finite time horizon dividendruin model where the firm pays out dividends to its shareholders according to a dividendbarrier strategy and becomes ruined when the firm asset value falls below the default threshold. The asset value process is modeled as a restricted Geometric Brownian process with an upper reflecting (dividend) barrier and a lower absorbing (ruin) barrier. Analytic solutions to the value function of the restricted asset value process are provided. We also solve for the survival probability and the expected present value of future dividend payouts over a given time horizon. The sensitivities of the firm asset value and dividend payouts to the dividend barrier, volatility of the firm asset value and firm’s credit quality are also examined. Key words: dividendruin model, dividend payouts, reflecting and absorbing barriers, survival probability
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"... Abstract. This paper investigates the optimal harvesting strategy for a single species living in random environments whose population growth is given by a regimeswitching diffusion. Harvesting acts as a (stochastic) control on the size of the population. The objective is to find a harvesting strate ..."
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Abstract. This paper investigates the optimal harvesting strategy for a single species living in random environments whose population growth is given by a regimeswitching diffusion. Harvesting acts as a (stochastic) control on the size of the population. The objective is to find a harvesting strategy which maximizes the expected total discounted income from harvesting up to the time of extinction of the species; the income rate is allowed to be state and environmentdependent. This is a singular stochastic control problem, with both the extinction time and the optimal harvesting policy depending on the initial condition. One aspect of receiving payments up to the random time of extinction is that small changes in the initial population size may significantly alter the extinction time when using the same harvesting policy. Consequently, one no longer obtains continuity of the value function using standard arguments for either regular or singular control problems having a fixed time horizon. This paper introduces a new sufficient condition under which the continuity of the value function for the regimeswitching model is established. Further, it is shown that the value function is a viscosity solution of a coupled system of quasivariational inequalities. The paper also establishes a verification theorem and, based on this theorem, an εoptimal harvesting strategy is constructed under certain conditions on the model. Two examples are analyzed in detail. Key words. regimeswitching diffusion, singular stochastic control, quasivariational inequality, viscosity solution, verification theorem
Harvesting in Stochastic Environments: Optimal Policies in a Relaxed Model
"... Abstract. This paper examines the objective of optimally harvesting a single species in a stochastic environment. This problem has previously been analyzed in [1] using dynamic programming techniques and, due to the natural payoff structure of the price rate function (the price decreases as the pop ..."
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Abstract. This paper examines the objective of optimally harvesting a single species in a stochastic environment. This problem has previously been analyzed in [1] using dynamic programming techniques and, due to the natural payoff structure of the price rate function (the price decreases as the population increases), no optimal harvesting policy exists. This paper establishes a relaxed formulation of the harvesting model in such a manner that existence of an optimal relaxed harvesting policy can not only be proven but also identified. The analysis imbeds the harvesting problem in an infinitedimensional linear program over a space of occupation measures in which the initial position enters as a parameter and then analyzes an auxiliary problem having fewer constraints. In this manner upper bounds are determined for the optimal value (with the given initial position); these bounds depend on the relation of the initial population size to a specific target size. The more interesting case occurs when the initial population exceeds this target size; a new argument is required to obtain a sharp upper bound. Though the initial population size only enters as a parameter, the value is determined in a closedform functional expression of this parameter. Key Words. Singular stochastic control, linear programming, relaxed control. AMS subject classification. 93E20, 60J60. 1
Optimal Dividend Policies for the PiecewiseDeterministic Compound Poisson Risk Model
, 2012
"... This paper deals with optimal dividend payment problem in the general setup of a piecewisedeterministic compound Poisson risk model. The objective of the insurance business model under consideration is to maximize the expected discounted dividend payout up to the time of ruin. We provide a comparat ..."
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This paper deals with optimal dividend payment problem in the general setup of a piecewisedeterministic compound Poisson risk model. The objective of the insurance business model under consideration is to maximize the expected discounted dividend payout up to the time of ruin. We provide a comparative study in this general framework of both restricted and unrestricted payment schemes, which were only previously treated separately in special cases of risk models in the literature. We prove with the generality of the piecewisedeterministic compound Poisson process the following results. In the case of restricted payment scheme, the value function is shown to be a classical solution of the corresponding HJB equation, which in turn leads to an optimal restricted payment policy known as the threshold strategy. The case of unrestricted payment scheme gives rise to a singular stochastic control problem. We solve the associated integrodifferential quasivariational inequality, which produces an optimal unrestricted dividend payment scheme known as the barrier strategy. When claim sizes are exponentially distributed, we offer general solutions to both dividend policies. Explicit expressions as well as numerical examples are presented for a number of practical applications. Key Words. Piecewisedeterministic compound Poisson model, optimal stochastic control, HJB equation, quasivariational inequality, threshold strategy, barrier strategy. AMS subject classifications. 93E20, 60J75 1
A Constrained Investment Policy for Defined – Contribution Pension Fund Management
"... This paper considered a stochastic control problem for the optimal management of a contribution pension fund model with solvency constraints. It is also strategic to accept the attitude of the fund manager who can invest in two assets: (a risky one and a non risky one in a standard Black Scholes mar ..."
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This paper considered a stochastic control problem for the optimal management of a contribution pension fund model with solvency constraints. It is also strategic to accept the attitude of the fund manager who can invest in two assets: (a risky one and a non risky one in a standard Black Scholes market) and maximize the utility function consequent upon the current level of fund wealth. Our aim in this paper is to pose a constraint on the fund manager by ensuring that a solvency level is maintained on the fund wealth. This implies that the wealth of the running pension fund remains above a stipulated level i.e. the solvency level.