Optimal cash management under uncertainty

We solve an agent’s optimization problem of meeting demands for cash over time with cash deposited in bank or invested in stock. The stock pays dividends and uncertain capital gains, and a commission is incurred in buying and selling of stock. We use a stochastic maximum principle to obtain explicitly the optimal transaction policy.     

Optimal control under persistent disturbances

Let f be an orientation-preserving Morse-Smale diffeomorphism of an n-dimensional (n ≥ 3) closed orientable manifold M ⁿ . We show the possibility of representing the dynamics of f in a “source-sink” form. The roles of the “source” and “sink” are played by invariant closed sets one of which, A _f , is an attractor, and the other, R _f , is a repeller. Such a representation reveals new topological invariants that describe the embedding (possibly, wild) of stable and unstable manifolds of saddle periodic points in the ambient manifold. These invariants have allowed us to obtain a classification of substantial classes of Morse-Smale diffeomorphisms on 3-manifolds. In this paper, for any n ≥ 3, we describe the topological structure of the sets A _f and R _f and of the space of orbits that belong to the set M ⁿ \ (A _f ∪ R _f ).     

Optimal investment under partial information

We consider the problem of maximizing terminal utility in a model where asset prices are driven by Wiener processes, but where the various rates of returns are allowed to be arbitrary semimartingales. The only information available to the investor is the one generated by the asset prices and, in particular, the return processes cannot be observed directly. This leads to an optimal control problem under partial information and for the cases of power, log, and exponential utility we manage to provide a surprisingly explicit representation of the optimal terminal wealth as well as of the optimal portfolio strategy. This is done without any assumptions about the dynamical structure of the return processes. We also show how various explicit results in the existing literature are derived as special cases of the general theory.     

Optimal XL-insurance under Wasserstein-type ambiguity

We study the problem of optimal insurance contract design for risk management under a budget constraint. The contract holder takes into consideration that the loss distribution is not entirely known and therefore faces an ambiguity problem. For a given set of models, we formulate a minimax optimization problem of finding an optimal insurance contract that minimizes the distortion risk functional of the retained loss with premium limitation. We demonstrate that under the average value-at-risk measure, the entrance-excess of loss contracts are optimal under ambiguity, and we solve the distributionally robust optimal contract-design problem. It is assumed that the insurance premium is calculated according to a given baseline loss distribution and that the ambiguity set of possible distributions forms a neighborhood of the baseline distribution. To this end, we introduce a contorted Wasserstein distance. This distance is finer in the tails of the distributions compared to the usual Wasserstein distance.     

Optimal strategies for water quality control

In this paper, the use of optimal control theory to obtain optimal strategies for the control of aquatic models is illustrated. Several types of control variables are used including the rate of nutrient application and the rates of change of nutrient concentration in both the phytoplankton and zooplankton populations. Techniques are given to show how optimal control theory can be applied to several models with different states and control variables constraints. Explicit expressions and optimality conditions are given for singular controls whenever they exist. Some numerical techniques are suggested to couple the optimal control parts in the proper sequence.     

Optimal vaccination patterns in age-structured populations: Endemic case

We consider a simple age-structured SIR model with vaccination and separable mixing. We define costs for a vaccination strategy (number of vaccinations per time) and effect (reduction of prevalence of disease or reduction of the number of risk cases). We consider two optimization problems: to find the strategy with minimal costs at a given level for the effect, and also to find the strategy with maximal effect at given costs. It turns out that there is an optimal strategy that is nonzero only in at most three age classes, i.e., consists of a sum of at most three delta-peaks.     

OPTIMAL REINSURANCE UNDER EXPECTED VALUE PRINCIPLE

The paper concerns the problem how to purchase the reinsurance in order to make the insurer and the reinsurance company＇s total risk to be least under the expected value principle. When the insurer and reinsurance company take arbitrary risk measures, sufficient con- ditions for optimality of reinsurance contract are given within the restricted class of admissible contracts. Further, the explicit forms of optimal reinsurance contract under several special risk measures are given, and the method to decide parameters as well.     

Optimal incremental learning under covariate shift

Learning strategies under covariate shift have recently been widely discussed. The density of learning inputs under covariate shift is different from that of test inputs. Learning machines in such environments need to employ special learning strategies to acquire greater capabilities of generalizing through learning. However, incremental learning methods are also used for learning in non-stationary learning environments, which represent a kind of covariate shift. However, the relation between covariate-shift environments and incremental-learning environments has not been adequately discussed. This paper focuses on the covariate shift in incremental-learning environments and our re-construction of a suitable incremental-learning method. Then, the model-selection criterion is also derived, which is to be an essential object function for memetic algorithms to solve these kinds of learning problems.     

Optimal sequential forestry decisions under risk

This paper is a summary of central and typical concepts, ideas and results in the field of sequential optimization and stochastic phenomena in forestry. The sequential optimization methods can be applied to all forestry decisions. The text covers forestry decisions and forest economics issues that are based on sequential decision making. An illustration covers optimal decisions in the presence of stochastic market prices. Stochastic (and/or deterministic but for different reasons unpredictable) changes in the economic and physical environments can be considered in decision making over time as soon as they are revealed. For this reason, the information and decision processes are sequential.     

Optimal risk retention under partial insurance

This paper examines the situation where a risk-averse insured determines the optimal amount of deductible (or stop-loss) insurance. The insurer uses two different premium principles, the expected value principle and the exponential principle. The insured has an exponential utility function. Specific numerical results are obtained for the optimal stop-loss limit in the case of a group life insurance plan. The exact results are contrasted with those obtained by using the normal approximation instead of the exact distribution of aggregate claims.     

Optimal reinsurance under risk and uncertainty

This paper deals with the optimal reinsurance problem if both insurer and reinsurer are facing risk and uncertainty, though the classical uncertainty free case is also included. The insurer and reinsurer degrees of uncertainty do not have to be identical. The decision variable is not the retained (or ceded) risk, but its sensitivity with respect to the total claims. Thus, if one imposes strictly positive lower bounds for this variable, the reinsurer moral hazard is totally eliminated.Three main contributions seem to be reached. Firstly, necessary and sufficient optimality conditions are given in a very general setting. Secondly, the optimal contract is often a bang–bang solution, i.e., the sensitivity between the retained risk and the total claims saturates the imposed constraints. Thirdly, the optimal reinsurance problem is equivalent to other linear programming problem, despite the fact that risk, uncertainty, and many premium principles are not linear. This may be important because linear problems may be easily solved in practice, since there are very efficient algorithms.     

Optimal control of inequality under uncertainty

We model the optimal control of inequality for an economy experiencing growth in the mean and variance of the income distribution under conditions of uncertainty. Given quadratic losses in the level of inequality and the strength of the policy instrument, we derive a closed form solution for the optimal policy rule in a finite time horizon model. A calibrated, numerical simulation derives the optimal rule required to return the United States to the level of inequality that it experienced in 1979.     

Optimal hedging under output price uncertainty

This paper provides a theoretical and empirical analysis of optimal hedging under output price uncertainty. The theoretical analysis is facilitated by exploiting the duality between production and cost while the empirical implementation uses the envelope theorem and the indirect expected utility function. Empirically estimable equations are derived by approximating the indirect expected utility function by a Taylor series approximation. The model is tested by using live cattle data as output while using prices of corn, soybeans, and the feeder cattle as inputs. The results support the theoretical predictions and the evidence shows that live cattle farmers exhibit decreasing absolute risk aversion.     

Optimal dividend-distribution strategy under ambiguity aversion

This paper considers the optimal dividend policy for an insurance company facing model uncertainty. We provide an explicit solution and show that an increase in ambiguity aversion leads to more conservative dividend policy. Interestingly, we find the ambiguity averse manager exhibits risk loving attitude when the company is close to bankruptcy. Finally, concerns about model misspecification have ambiguous effects on the marginal value of cash, which depends on the cash reserve.     

基于夏普比率的最优再保险策略

当保险公司承保巨灾风险时,通过再保险转移风险是非常必要的。再保险是保险人将其承保业务的一部分转移给再保险人的行为,而再保险业务中核心是最优再保险策略问题,即以何种形式分保以及具体分保的额度。本文引入基金业中风险管理和绩效评估等方面常用的指标-夏普比率,构建了基于该指标的再保险策略风险模型.对于分保业务中常见的两种形式:成数再保险和止损再保险,文章通过分析得出使得保险人夏普比率最大化的风险自留比率和风险自留额度。基于夏普比例对最优再保险策略的研究可以为保险公司的再保险业务提供决策依据。     

Optimal reinsurance under dynamic VaR constraint

This paper deals with the optimal reinsurance strategy from an insurer’s point of view. Our objective is to find the optimal policy that maximises the insurer’s survival probability. To meet the requirement of regulators and provide a tool to risk management, we introduce the dynamic version of Value-at-Risk (VaR), Conditional Value-at-Risk (CVaR) and worst-case CVaR (wcCVaR) constraints in diffusion model and the risk measure limit is proportional to company’s surplus in hand. In the dynamic setting, a CVaR/wcCVaR constraint is equivalent to a VaR constraint under a higher confidence level. Applying dynamic programming technique, we obtain closed form expressions of the optimal reinsurance strategies and corresponding survival probabilities under both proportional and excess-of-loss reinsurance. Several numerical examples are provided to illustrate the impact caused by dynamic VaR/CVaR/wcCVaR limit in both types of reinsurance policy.     

Optimal velocity functions under energy regeneration

Energy conservation for a subway system can be achieved through implementation of regenerative braking. In the context of natural receptivity, the regenerated energy may be used to supply the power need of nearby trains. Minimization of effective energy usage is examined and such optimal modes of operation of an individual train between a pair of stations are derived for various degrees of regeneration.