On mean-variance portfolio selection under a hidden Markovian regime-switching model

We study a mean-variance portfolio selection problem under a hidden Markovian regime-switching Black–Scholes–Merton economy. Under this model, the appreciation rate of a risky share is modulated by a continuous-time, finite-state hidden Markov chain whose states represent different states of an economy. We consider the general situation where an economic agent cannot observe the “true” state of the underlying economy and wishes to minimize the variance of the terminal wealth for a fixed level of expected terminal wealth with access only to information about the price processes. By exploiting the separation principle, we discuss the mean-variance portfolio selection problem and the filtering-estimation problem separately. We determine an explicit solution to the mean-variance problem using the stochastic maximum principle so that we do not need the assumption of Markovian controls. We also provide robust estimates of the hidden state of the chain and develop a robust filter-based EM algorithm for online recursive estimates of the unknown parameters in the model. This simplifies the filtering-estimation problem.     

Optimal investment and consumption strategies with state-dependent utility functions and uncertain time-horizon

This paper considers the multi-period optimal strategies for an investment-only problem and an investment–consumption problem. The financial market is regime-switching and consists of one risk-free asset and multiple risky assets. The state process of the financial market is modeled by a finite-state Markov chain. Asset returns and utility functions are affected by the states of the financial market. The investment time-horizon is uncertain and exogenous. By adopting the dynamic programming approach, explicit expressions for optimal value functions and optimal investment and consumption strategies are derived. Moreover, some discussions and numerical examples are provided to illustrate our results, which extend some results in the existing literature to more general situations and show some interesting phenomena.     

Multi-period Markowitz's mean–variance portfolio selection with state-dependent exit probability

This paper considers a multi-period mean–variance portfolio selection problem with uncertain time-horizon in a regime-switching market, where the conditional distribution of the time-horizon is assumed to be stochastic and depends on the market states as the returns of risky assets do. Existence of the optimal investment strategy is analyzed, and the closed-form expressions for the optimal investment strategy and the efficient frontier are derived. In addition, some interesting properties of the efficient frontier are illustrated by numerical analysis and by comparing with the efficient frontier of the case where the distribution of the uncertain time-horizon does not depend on market states.     

生命周期、风险偏好和积累水平对DC型养老金资产配置策略的影响研究*

近年来,DC型养老金在我国得到了长足发展。DC型养老金的积累期长达数十年,如何通过有效的资产配置,实现参保人更高的养老效用是理论界和实务界都关注的问题。本文在默顿（Merton）连续时间最优投资-消费问题框架下,建立了DC型养老金最优资产配置问题的随机优化模型。以此为基础,本文研究了生命周期、风险偏好和积累水平对养老金积累期最优资产配置策略的影响。进而,通过Monte Carlo模拟,本文研究了最优资产配置策略与恒定资产配置比例策略下养老金积累效果的优劣。本文的结论证明,在放开DC型养老金投资限制的条件下,引入“生命周期基金”和“生命特征基金”,引导最优资产配置很有必要。     

Optimal Controls for a Large Insurance Under a CEV Model: Based on the Legendre Transform-Dual Method

The purpose of this paper is to consider the optimal proportional reinsurance and investment strategies for an insurance company. The insurer’s surplus process is approximated by a Brownian motion with drift. The insurance company can purchase proportional reinsurance and invest the surplus in a financial market which includes one risk-free asset and one risky asset whose price is modeled by a CEV model. The primary problem is changed to the dual problem by implying Legendre transform. When the objective of the insurance company is to maximize the expected logarithmic utility from terminal wealth, the closed-form expressions for the optimal reinsurance-investment policy which is different to the Merton case to the primal optimal problem are obtained and numerical simulations are provided to demonstrate our results. Moreover, we find an interesting result that risk exposure is non-monotonic in the cost of reinsurance.

     

Pricing bond options under a Markovian regime-switching Hull–White model

In this paper, we investigate the valuation of bond options under a Markovian regime-switching Hull–White model, where both the mean-reverting level and the volatility of the interest rate are modulated by a continuous-time, finite-state Markov chain. Using techniques of measure changes and the inverse Fourier transform, we obtain an integral representation for the pricing formula of a standard European option on a zero-coupon bond. Numerical results for the prices and implied volatilities of bond options arising in our model are given in a two-regime case.     

Long-term investment with stochastic interest and inflation rates: The need for inflation-indexed bonds

We examine the long term investment problem, under stochastic interest and inflation rates and within financial market incompleteness. Four basic financial assets are available on the financial market: a money market account (the cash), a real consumption good, a financial stock index and a bond with constant maturity. In this incomplete framework, we provide the general solution of the expected utility maximization. We compute the monetary loss from not having access to an inflation-indexed bond, in order to be hedged against the inflation risk. We show that this latter one usually reaches high levels (more than 1% per year). Thus, the magnitude of such costs reaches those of management fees or transaction costs. They highlight the significant value of introducing inflation-indexed bonds in the financial markets.     

Optimal fiscal policy, uncertainty, and growth

This paper analyzes the macroeconomic effects of fiscal policy in a stochastic endogenous growth model. Due to externalities in human capital accumulation, the market allocation is inefficient, thereby justifying government intervention. The uncertainty stemming from technological disturbances affects the growth rate, which can be explained by precautionary motives of risk averse agents. Fiscal policy means consist of a consumption tax, investment subsidies, and bonds. We obtain counter-acting growth effects of investment subsidies, which are differentiated with respect to deterministic and stochastic capital income components. The policy implications from the deterministic model are substantially extended in the stochastic context. A general rule for a welfare maximizing policy is derived, which is represented by a continuum of alternative tax-transfer-schemes. We discuss three benchmark cases, which crucially differ with respect to their implications regarding the size of the government expenditure share.     

Asset prices and economic fluctuations: The implications of stochastic volatility

This paper investigates whether the multi-factor stochastic volatility of stock returns is related to economic fluctuations and affects asset prices. We address these issues in a dynamic Fama-French three-factor volatility model framework. Consistent with the ICAPM with stochastic volatility (Campbell et al., 2017), we find that the conditional volatility of the size and value factors is significantly related to economic uncertainty. These volatilities are also significant pricing factors. The out-of-sample forecasting analysis further reveals that the conditional volatility can predict stock returns and deliver economic gain in asset allocation. Our analysis sharpens the understanding on the link between the stock market and economic fundamentals.     

资产管理中客户偏好的研究——兼论考虑偏好条件下基金的评估

本文探讨了资产管理中确定客户偏好和根据客户偏好选择最适合客户的资产配置方案的方法 ;并给出一个资产管理中关于波动风险偏好的随机动态模型 ,推广了R .C .Merton( 1 970 )的模型。原模型是关于消费和投资组合的动态经济模型。笔者修改了效用函数和约束方程 ,去掉消费变量并加入波动风险偏好因素 ,得到风险资产的比例和客户波动风险偏好的关系 ,以及和时间偏好之间的关系。最后论述了在考虑投资者偏好条件下 ,证券投资基金的评估方法 ,以及实际案例。     

Investment horizon effect on asset allocation between value and growth strategies

How does the optimal risk exposure of assets change as their investment horizons increase? Does this impact investment portfolio decision-making, in particular, optimal asset allocation between value and growth strategies over various investment horizons? This paper adopts a new approach to address these questions by examining portfolio allocation between value and growth stocks over various investment horizons. This new approach is based on wavelet analysis, which decomposes the returns of a particular investment strategy across multiple investment horizons. The key empirical results show that the success of pursuing the value strategy (short-selling growth stocks and going long on value stocks) is impacted by the approach used to classify value and growth stock returns. We explore two common alternatives: Fama-French versus Standard & Poor's (S&P) 500/Barra portfolios. The results using Fama-French portfolios show that as the investment horizon increases, the optimal mean allocation of investors tilts heavily away from growth stocks, particularly for lower and moderate levels of risk aversion. Interestingly, for S&P 500/Barra portfolios the allocation weights between value and growth do not vary much.     

Analysis of the Interaction between Regional R&D Productivity and the Investment Strategies of Multinational Enterprises

The aim of this article is to analyze the interaction between regional R&D productivity and the investment strategies of multinational enterprises. The discussion is based on the hypothesis that R&D investments cause a reduction in the production costs and an increase in firms’ market share; furthermore, R&D costs may be affected by national industrial policies. Supposing the existence of asymmetries in local research productivity, necessary and sufficient conditions for a geographical diversification of resources have been found. Suggestions with respect to the optimal allocation of R&D investment are finally derived.     

International portfolio reallocation: Diversification benefits and European monetary union

We investigate the determinants of bilateral international equity and bond portfolio reallocation across a large cross-section of countries spanning over two sample periods: 1997-2001 and 1997-2005. We find that the strongest drivers are the marginal diversification benefits arising from the pure asset component and the initial degree of underweight. This evidence suggests that global portfolio reallocations over the asset boom and bust period were determined by optimal diversification considerations. We also find that due to economic and monetary union (EMU) the weight assigned by euro area investors to investment in euro area countries increased significantly in equity and fixed income portfolios, with a trade diverting effect against the British bond market.     

Optimal stopping time with stochastic volatility

This paper demonstrates how to convert a path-dependent optimal stopping time problem into a path-independent problem using a transformation analysis method. We test this method to deal with several problems, especially those in stochastic volatility environments. We introduce stochastic state variables into volatility dynamics and analyse the influence of state-variable volatile characters on investment stopping boundaries. For arbitrary coefficient circumstances, we set up a Riccati equation that satisfies the transformation. For circumstances involving Heston stochastic-volatility, we propose an analytical solution. This paper extends research on the optimal investment stopping issue to a stochastic investment opportunity environment. Our proposed method can enhance the ability of optimal investment stopping theory to describe the real capital market.     

Discrete-time optimal asset allocation under Higher-Order Hidden Markov Model

This paper studies an optimal portfolio selection problem under a discrete-time Higher-Order Hidden Markov-Modulated Autoregressive (HO-HMMAR) model for price dynamics. By interpreting the hidden states of the modulating higher-order Markov chain as different states of an economic condition, the model discussed here may incorporate the long-term memory of economic states in modeling price dynamics and optimal asset allocation. The estimation of an estimation method based on Expectation-Maximization (EM) algorithm is used to estimate the model parameters with a view to reducing numerical redundancy. The asset allocation problem is then discussed in a market with complete information using the standard Bellman's principle and recursive formulas are derived. Numerical results reveal that the HO-HMMAR model may have a slightly better out-of-sample forecasting accuracy than the HMMAR model over a short horizon. The optimal portfolio strategies from the HO-HMMAR model outperform those from the HMMAR model without long-term memory in both real data and simulated data experiments.     

Optimal gradual liquidation of equity from a risky asset

We consider a problem of optimal gradual liquidation of equity from a risky asset for continuous time stochastic market model. The owner of the risky asset uses this equity as a source of steady cash flow by borrowing money permanently against this equity. At the terminal time, there is no equity for him in this asset, and the bank gains ownership of this asset. Optimal strategy is obtained explicitly.     

Evolution,finance, and the population genetics of relative wealth

Attempts to use evolutionary ideas in finance have often neglected mathematical population genetics. Population genetics provides a natural approach to certain problems in finance that involve the relative wealth that accrues to competing investment strategies. In our model, competing investment strategies differ only in their allocation to a risky asset versus a riskless asset. Here we use results from the population genetics of natural selection to find the investment strategy that maximizes the expected increase in relative wealth. Though we focus on single-period analysis, some of our key findings are reminiscent of those from the growth optimal portfolio literature, e.g., the Kelly criterion.     

Rational inattention,long-run consumption risk,and portfolio choice

This paper explores how the introduction of rational inattention (RI) – that agents process information subject to finite channel capacity – affects optimal consumption and investment decisions in an otherwise standard intertemporal model of portfolio choice. We first explicitly derive optimal consumption and portfolio rules under RI and then show that introducing RI reduces the optimal share of savings invested in the risky asset because inattentive investors face greater long-run consumption risk. We also show that the investment horizon matters for portfolio allocation in the presence of RI, even if investment opportunities are constant and the utility function of investors is constant relative risk aversion. Second, after aggregating across investors, we show that introducing RI can better explain the observed joint dynamics of aggregate consumption and the equity return. Finally, we show that RI increases the implied equity premium because investors under RI face greater long-run consumption risk and thus require higher compensation in equilibrium.     

Uncertainty in the public debt market and stochastic long-run growth

In a continuous time model, a representative household has to allocate its investment and consumption in an optimal manner under conditions of uncertainty. In the present study it is hypothesized that there are two types of assets: a risk-free and a risky asset. The risk-free asset is assumed to be the physical capital, while at the same time uncertainty is allowed to result from the exogenous random variations in the public debt market, rendering in this way government bonds to act as the risky asset. In the endogenous growth framework with productive public investment, the expected long-run growth rate, the dynamic path of consumption as well as the optimal allocation of investment between a risky and a riskless asset, are analytically derived. This kind of treatment allows us to create a locus for the long-run growth over the various levels of uncertainty. The outcome of the analysis is that a rise in uncertainty impacts negatively upon the long-run growth rate. In order to empirically assess the relationship between growth and uncertainty, we lay our emphasis on the US economy for the period 1957:1 to 2008:4. Within the framework of a bivariate BEKK–GARCH(1,1)-M model a significant negative relationship between uncertainty and economic growth has been established.     

保险公司不动产最优投资策略研究*

本文研究了保险公司投资不动产时的最优投资策略问题。本文假设保险公司的风险过程为经典Cramer Lundeberg模型。保险公司可把资金投资于现金市场和两个风险市场，分别为债券、股票和不动产。在卖空、借贷限制下，基于均值—方差模型，应用辅助随机二次线性问题求解方法，得到最优投资策略和有效边界。研究结果显示，不动产最优投资量不仅与初始资本金存在非简单线性关系，还与不动产的市场溢价水平、未预期冲击存在一系列复杂关系。