Alpha-robust mean-variance reinsurance-investment strategy

Inspired by the α-maxmin expected utility, we propose a new class of mean-variance criterion, called α-maxmin mean-variance criterion, and apply it to the reinsurance-investment problem. Our model allows the insurer to have different levels of ambiguity aversion (rather than only consider the extremely ambiguity-averse attitude as in the literature). The insurer can purchase proportional reinsurance and also invest the surplus in a financial market consisting of a risk-free asset and a risky asset, whose dynamics is correlated with the insurance surplus. Closed-form equilibrium reinsurance-investment strategy is derived by solving the extended Hamilton–Jacobi–Bellman equation. Our results show that the equilibrium reinsurance strategy is always more conservative if the insurer is more ambiguity-averse. When the dependence between insurance and financial risks are weak, the equilibrium investment strategy is also more conservative if the insurer is more ambiguity-averse. However, in order to diversify the portfolio, a more ambiguity-averse insurer may adopt a more aggressive investment strategy if the insurance market is very ambiguous. For an ambiguity-neutral insurer, the investment strategy is identical to the non-robust investment strategy.     

On pre-commitment aspects of a time-consistent strategy for a mean-variance investor

In this paper, a link between a time-consistent and a pre-commitment investment strategy is established. We define an implied investment target, which is implicitly contained in a time-consistent strategy at a given time step and wealth level. By imposing the implied investment target at the initial time step on a time-consistent strategy, we form a hybrid strategy which may generate better mean-variance efficient frontiers than the time-consistent strategy. We extend the numerical algorithm proposed in Cong and Oosterlee (2016b) to solve constrained time-consistent mean-variance optimization problems. Since the time-consistent and the pre-commitment strategies generate different terminal wealth distributions, time-consistency is not always inferior to pre-commitment.     

Equilibrium mean–variance reinsurance and investment strategies for a general insurance company under smooth ambiguity

This work investigates the equilibrium investment and reinsurance strategies for a general insurance company under smooth ambiguity. The general insurance company holds shares of an insurance company and a reinsurance company. The claims of the insurer follow a compound Poisson process. The insurer can divide part of the insurance risk to the reinsurer. Besides, the insurer and reinsurer both participate in the financial market and invest in cash and stock. However, the general insurance company is ambiguous about the insurance and financial risks and is an ambiguity-averse manager (AAM). The uncertainties over the insurance and financial risks are described by second-order distributions. The AAM aims to maximize the average performance of the weighted sum surplus process of the insurer and reinsurer under the mean–variance criterion and smooth ambiguity. We present the extended Hamilton–Jacobi–Bellman (HJB) system for the optimization problem combining the mean–variance criterion and smooth ambiguity. In the case that the second-order distributions are Gaussian, we obtain the closed-forms of the equilibrium reinsurance and investment strategies. At the end of this work, sensitivity analyses are presented to show the economic behaviors of the AAM.     

Optimal investment and reinsurance policies for an insurer with ambiguity aversion

In this paper, we study the optimal investment and reinsurance problem for an insurer based on the variance premium principle, in which three cases are considered. First, we assume that the financial market does not exist. The insurer only holds an insurance business, and the optimal reinsurance problem is studied. Subsequently, we assume that there exists a financial market with an accurately modeled risky asset. The optimal investment and reinsurance problem is investigated under these conditions. Finally, we consider the general case in which the insurer is concerned about the model ambiguity of both the insurance market and the financial market. In all three cases, the value function is set to maximize the expected utility of terminal wealth. By employing the dynamic programming principle, we derive the Hamilton–Jacobi–Bellman (HJB) equations, which are satisfied by the value functions and obtain closed-form solutions for optimal reinsurance and investment policies and the value functions in all three cases. Most interestingly, we elucidate how investment improves the insurer’s utility and find that the existence of ambiguity can significantly affect the optimal policies and value functions. We also compare the ambiguities in the two markets and find that ambiguity in the insurance market has much more significant impact on the value function than the ambiguity in the financial market. It implies that it is more valuable for insurer to precisely evaluate the insurance risk. We also provide some numerical examples and economic explanations to illustrate our results.     

Optimal time-consistent reinsurance and investment strategies for a jump–diffusion financial market without cash

This paper considers an optimal reinsurance and investment strategies for an insurer under mean–variance criterion within a game theoretic framework. Specially, it is assumed that the surplus process is governed by a Cramér–Lundberg model, and apart from purchasing reinsurance, the insurer is allowed to invest in a financial market with multiple assets that all can be risky, whose price processes are modeled by the jump–diffusion process. Due to the market without cash, the method of separating the variables is not viable any more. We turn to an alternative approach to solve the extended Hamilton–Jacobi–Bellman equation, and closed-form expressions of the optimal strategies and value function are not only derived but also proved to be uniqueness. Moreover, some special cases of our model are provided and several numerical analyses for our results are presented as well. Under this criterion, different from existing literature, we find that (i) the value function is not linear but quadratic with respect to the current wealth; (ii) the optimal reinsurance and investment strategies depend on the wealth process; (iii) the parameters of risky assets(insurance market) have impacts on the optimal reinsurance(investment) policy; (iv) the safety loading of the insurer affects the optimal strategies.     

An analytical solution for the robust investment-reinsurance strategy with general utilities

In financial markets, different investors have different attitudes or preferences on the investment policies and reinsurance problems. For investors with different investment utilities, how to provide an optimal investment strategy is not only a very hard problem, but also an urgent problem to be solved. In this paper, we derive an analytical solution for the optimal allocation problem of investment-reinsurance with general-form utility function. The general utility function allows for varying relative risk aversion coefficient, which is an important feature in finance theory. However, obtaining analytical solutions for general utility function has been difficult or impossible. The solution presented in this paper is constructed through the homotopy analysis method (HAM) and written in the form of a Taylor series expansion. The fully nonlinear Hamilton–Jacobi–Bellman (HJB) equation is decomposed into an infinite series of linear PDEs, which can be solved analytically. In the end, three examples are presented to illustrate the convergence and accuracy of the method, it also demonstrates that different risk reference investors have different investment-reinsurance strategies.     

Mean-variance portfolio selection of cointegrated assets

This paper considers the continuous-time mean-variance portfolio selection problem in a financial market in which asset prices are cointegrated. The asset price dynamics are then postulated as the diffusion limit of the corresponding discrete-time error-correction model of cointegrated time series. The problem is completely solved in the sense that solutions of the continuous-time portfolio policy and the efficient frontier are obtained as explicit and closed-form formulas. The analytical results are applied to pairs trading using cointegration techniques. Numerical examples show that identifying a cointegrated pair with a high mean-reversion rate can generate significant statistical arbitrage profits once the current state of the economy sufficiently departs from the long-term equilibrium. We propose an index to simultaneously measure the departure level of a cointegrated pair from equilibrium and the mean-reversion speed based on the mean-variance paradigm. An empirical example is given to illustrate the use of the theory in practice.     

Market selection of constant proportions investment strategies in continuous time

This paper studies the wealth dynamics of investors holding self-financing portfolios in a continuous-time model of a financial market. Asset prices are endogenously determined by market clearing. We derive results on the asymptotic dynamics of the wealth distribution and asset prices for constant proportions investment strategies. This study is the first step towards a theory of continuous-time asset pricing that combines concepts from mathematical finance and economics by drawing on evolutionary ideas.     

The effects of uncertainty on investment and the expected long-run capital stock

This paper examines the effects of output price uncertainty on the optimal investment behavior of a risk-neutral competitive firm with a constant returns to scale production function. In the presence of convex costs of adjustment, investment is an increasing function of q, the shadow price of capital. Given the current price of output, we find that increased uncertainty will raise the current rate of investment. Increased uncertainty will also increase the expected long-run capital stock if the price of output is serially uncorrelated. However, if the price of output is serially correlated, then the direction of the effect of increased uncertainty on the expected long-run capital stock depends on the curvature of the marginal adjustment cost function. In this case, we obtain results which are directly opposite of the results in the literature and we locate the flaw in the existing analysis.     

Optimal consumption and investment under partial information

We consider a stock market model where prices satisfy a stochastic differential equation with a stochastic drift process. The investor’s objective is to maximize the expected utility of consumption and terminal wealth under partial information; the latter meaning that investment decisions are based on the knowledge of the stock prices only. We derive explicit representations of optimal consumption and trading strategies using Malliavin calculus. The results apply to both classical models for the drift process, a mean reverting Ornstein-Uhlenbeck process and a continuous time Markov chain. The model can be transformed to a complete market model with full information. This allows to use results on optimization under convex constraints which are used in the numerical part for the implementation of more stable strategies. Supported by the Austrian Science Fund FWF, project P17947-N12. We thank two anonymous referees for their comments which led to a considerable improvement of the paper.     

Optimal investment decisions when time-horizon is uncertain

Many investors do not know with certainty when their portfolio will be liquidated. Should their portfolio selection be influenced by the uncertainty of exit time? In order to answer this question, we consider a suitable extension of the familiar optimal investment problem of Merton [Merton, R.C., 1971. Optimal consumption and portfolio rules in a continuous-time model. Journal of Economic Theory 3, 373–413], where we allow the conditional distribution function of an agent’s time-horizon to be stochastic and correlated to returns on risky securities. In contrast to existing literature, which has focused on an independent time-horizon, we show that the portfolio decision is affected.     

The risk-return trade-off in human capital investment

In this paper, we analyze investments in human capital in a way which is standard for financial assets, but not (yet) for human capital assets. We study mean-variance plots of human capital assets. We compare the properties of human capital returns using a performance measure and by using tests for mean-variance spanning. Fields differ strongly not only in common rates of return, but also in return per unit of risk. We identify a range of educations that are efficient in terms of investment goods, and a range of educations that may be chosen for consumption purposes.     

A patent race in a real options setting: Investment strategy, valuation, CAPM beta, and return volatility

In this paper, we study financial properties of R&D intensive firms through a continuous-time real-options patent-race model. Numerical analysis in this study shows that intense competition drives a firm to invest more aggressively, which then pushes up its cost of capital and return volatility while introducing negative return correlation with its competitor. Furthermore, we find that a firm's position in competition has important impacts on its financial properties. For instance, a firm's cost of capital is a non-monotonic function of its relative position in the race. In addition, the relationship between cash flow uncertainty and investment can be negative when a firm is far ahead or far behind, or positive when firms are close in the race.     

Using difference equations to find optimal tax structures on the SugarScape

The use of equations to describe agent-based model dynamics allows access to mathematical theory that is not otherwise available. In particular, equation models can be effective at solving optimization problems—that is, problems concerning how an agent-based model can be most effectively steered into a particular state. In order to illustrate this strategy, we describe a modified version of the well-known SugarScape model and implement taxation. The optimization problem is to determine tax structures that minimize deaths but maximize tax income. Tax rates are dependent upon the amount of sugar available in a particular region; the rates change over time. A system of discrete difference equations is built to capture agent-based model dynamics. The equations are shown to capture the dynamics very well both with and without taxation. A multi-objective optimization technique known as Pareto optimization is then used to solve the problem. Rather than focusing on a cost function in which the two objectives are assigned weights, Pareto optimization is a heuristic method that determines a suite of solutions, each of which is optimal depending on the priorities of the researcher. In this case, Pareto optimization allows analysis of the tradeoff between taxes collected and deaths caused by taxation. The strategies contained here serve as a framework for a broad class of models.     

VaR约束下的投资组合决策模型分析

VaR方法是目前国际上风险管理的主流方法之一。文章将VaR应用到Markwitz均值-方差模型中,构建和动态调整了投资者的最优投资组合,并分析了该组合模型的特性,提出了应用模型中应注意的问题。     

Utility indifference valuation for jump risky assets

We discuss utility maximization problems with exponential preferences in an incomplete market where the risky asset dynamics is described by a pure jump process driven by two independent Poisson processes. This includes results on portfolio optimization under an additional European claim. Value processes of the optimal investment problems, optimal hedging strategies and the indifference price are represented in terms of solutions to backward stochastic equations driven by the Poisson martingales. Via a duality result, the solution to the dual problems is derived. In particular, an explicit expression for the density of the minimal martingale measure is provided. The Markovian case is also discussed. This includes either asset dynamics dependent on a pure jump stochastic factor or claims written on a correlated non tradable asset.     

基于运筹优化的物流与设施规划课程教学研究

在传统教学中,物流与设施规划课程的物流分析、设施布局等内容的一些经典问题采用启发式方法或试验法来解决。为了更精确地解决这些问题,采用数学规划方法提供解决方案。主要围绕建模技巧、应用软件教学和解决物流与设施规划专业案例等方面培养学生运用优化原理与方法构建运筹优化模型的能力以及运用ILOG OPL优化软件解决实际优化问题的能力。以二次分配问题和多产品工艺过程图优化问题为案例阐述了数学规划建模和编程求解的过程。     

Investment behaviour and “bull & bear” dynamics: modelling real and stock market interactions

In this article, we develop a simple behavioural macrodynamic model in continuous-time with the purpose of investigating the interaction of the real economy and the financial markets. Building on Westerhoff (Discret Dyn Nat Soc, 2012), we improve the specification of aggregate demand by distinguishing between consumption and investment expenditure and assuming that the latter is determined by the flexible accelerator principle. We remove the ad hoc nonlinearity in the fundamentalist behavioural rule and allow the composition of the population between chartists and fundamentalists to be endogenously determined. The resulting nonlinear dynamic systems are shown to generate various dynamic regimes, among which the coexistence of periodic attractors with interesting economic implications. Endogenous investment and stock market dynamics emerge, procyclical to each other, reflecting the interaction of induced investment with alternating waves in speculators’ sentiments. We show that a strong investment accelerator might be a crucial force generating fluctuations that, on the one hand, are transmitted and amplified by chartists and, on the other hand, are contained by fundamentalists.

     

Social responsibility portfolio optimization incorporating ESG criteria

Social responsibility investment (SRI) has attracted worldwide attention for its potential in promoting investment sustainability and stability. We developed a three-step framework by incorporating environmental, social, and governance (ESG) performance into portfolio optimization. In comparison to studies using weighted ESG rating scores, we constructed a data envelopment analysis (DEA) model with quadratic and cubic terms to enhance the evidence of two or more aspects, as well as the interaction between the environmental, social, and governance attributes. We then combined the ESG scores with financial indicators to select assets based on a cross-efficiency analysis. The portfolio optimization model incorporating ESG scores with selected assets was constructed to obtain a social responsibility investment strategy. To illustrate the effectiveness of the proposed approach, we applied it in the United States industrial stock market from 2005 to 2017. The empirical results show that the obtained SRI portfolio may be superior to traditional investment strategies in many aspects and may simultaneously achieve the consistency of investment and social values.