Demand for insurance in a portfolio setting

This paper takes an additional step toward analyzing the demand for insurance in the context of a portfolio model. An investor is endowed with a portfolio containing a risky and riskless asset that can be augmented by purchasing insurance. Here, insurance is paid for by reducing the quantity of the risky insurable asset, holding the quantity of the riskless asset fixed. In the standard insurance demand model, insurance is paid for by reducing the amount of the riskless asset. This distinction leads to a different insurance demand function because the opportunity cost of purchasing insurance is now random.     

Optimal investment for insurers

We consider a stochastic model for the wealth of an insurance company which has the possibility to invest into a risky and a riskless asset under a constant mix strategy. The total insurance claim amount is modeled by a compound Poisson process and the price of the risky asset follows a geometric Brownian motion. We investigate the resulting integrated risk process and the corresponding discounted net loss process. This opens up a way to measure the risk of a negative outcome of the integrated risk process in a stationary way. We provide an approximation of the optimal investment strategy, which maximizes the expected wealth under a risk constraint on the Value-at-Risk.     

Minimizing the Probability of Ruin When Consumption is Ratcheted

Abstract

We assume that an agent’s rate of consumption is ratcheted; that is, it forms a nondecreasing process. We assume that the agent invests in a financial market with one riskless and one risky asset, with the latter’s price following geometric Brownian motion as in the Black-Scholes model. Given the rate of consumption, we act as financial advisers and find the optimal investment strategy for the agent who wishes to minimize his probability of ruin. To solve this minimization problem, we use techniques from stochastic optimal control.     

资本约束对商业银行资产配置行为的影响——基于175家商业银行数据的经验研究

本文使用1998～2009年我国175家商业银行的资产配置数据,研究了资本监管制度对银行资产配置行为的影响。本文发现,现行的资本监管制度对银行资产配置行为具有重要影响,资本监管制度实施之后,银行依据自身资本水平调整资产结构,资本充足银行持有更多的风险资产,贷款比例较高;而资本不足银行则减持风险资产,贷款比例下降。此外,由于不同规模商业银行面临的融资约束不同,资本水平对资产配置行为的影响存在一定的差异,资本对城市及农村商业银行的约束效应更明显。本文的这些发现为监管当局的资本监管政策提供了经验证据,并提出进行差异化监管的政策建议。     

Investment Horizon Effects

Abstract:   Boudry and Gray (2003) have documented that the optimal buy‐and‐hold demand for Australian stocks is not necessarily increasing in the investment horizon when returns are predictable. Such finding is in contrast with Barberis (2000) who shows that positive monotonic horizon effects predominate for US stocks. Using a closed‐form approximation to the asset allocation problem, this paper relates the return dynamics to the investor's portfolio choice for different investment horizons. In the special case of a single risky asset, it is shown that return predictability under stationarity may induce both positive and negative horizon effects in the optimal allocation to the risky asset. The paper extends previous empirical results by solving for the optimal portfolio when two risky assets with predictable returns are available for investment.     

Ordering Uncertain Options under Inflation: A Note

Stochastic dominance rules (SD) have been extended to the case where investors are allowed to borrow and lend at the riskless interest rate. Stochastic dominance rules with a riskless asset (SDR) are much more effective than SD rules. However, it seems that this benefit is eliminated by an uncertain inflation, since riskless assets become risky once uncertain inflation is considered. We prove in this paper that SDR criteria are valid also in the face of uncertain (and independent) inflation. Moreover, while the mean-variance (MV) efficient set increases with uncertain inflation, the stochastic dominance efficient sets decrease.     

Optimal Portfolio Selection with Transaction Costs

Abstract

This paper examines the lifetime portfolio-selection problem in the presence of transaction costs. Using a discrete time approach, we develop analytical expressions for the investor's indirect utility function and also for the boundaries of the no-transactions region. The economy consists of a single risky asset and a riskless asset. Transactions in the risky asset incur proportional transaction costs. The investor has a power utility function and is assumed to maximize expected utility of end-of-period wealth. We illustrate the solution procedure in the case in which the returns on the risky asset follow a multiplicative binomial process. Our paper both complements and extends the recent work by Gennotte and Jung (1994), which used numerical approximations to tackle this problem.     

Pension funds with a minimum guarantee: a stochastic control approach

In this paper we propose and study a continuous-time stochastic model of optimal allocation for a defined contribution pension fund with a minimum guarantee. We adopt the point of view of a fund manager maximizing the expected utility from the fund wealth over an infinite horizon. In our model the dynamics of wealth takes directly into account the flows of contributions and benefits, and the level of wealth is constrained to stay above a “solvency level.” The fund manager can invest in a riskless asset and in a risky asset, but borrowing and short selling are prohibited. We concentrate the analysis on the effect of the solvency constraint, analyzing in particular what happens when the fund wealth reaches the allowed minimum value represented by the solvency level.     

Portfolio optimization under a generalized hyperbolic skewed t distribution and exponential utility

In this paper, we show that if asset returns follow a generalized hyperbolic skewed t distribution, the investor has an exponential utility function and a riskless asset is available, the optimal portfolio weights can be found either in closed form or using a successive approximation scheme. We also derive lower bounds for the certainty equivalent return generated by the optimal portfolios. Finally, we present a study of the performance of mean–variance analysis and Taylor’s series expected utility expansion (up to the fourth moment) to compute optimal portfolios in this framework.     

Asset liquidity,business risk,and beta

Extant literature posits that because of leverage, equity beta estimates from a single factor capital asset pricing model based on an equity-only market index are biased. We show analytically that this leverage bias is intimately related to the firm's asset structure per se, the firm's asset liquidity (i.e., cash holdings) and business risk. This is mainly because riskless cash holdings and risky real assets jointly determine the relevant risk for asset pricing. We empirically confirm that asset liquidity and business risk can marginally explain the leverage bias in the cross-section of stocks returns.     

Optimal constrained investment in the Cramer-Lundberg model

We consider an insurance company whose surplus is represented by the classical Cramer-Lundberg process. The company can invest its surplus in a risk-free asset and in a risky asset, governed by the Black-Scholes equation. There is a constraint that the insurance company can only invest in the risky asset at a limited leveraging level; more precisely, when purchasing, the ratio of the investment amount in the risky asset to the surplus level is no more than a; and when short-selling, the proportion of the proceeds from the short-selling to the surplus level is no more than b. The objective is to find an optimal investment policy that minimizes the probability of ruin. The minimal ruin probability as a function of the initial surplus is characterized by a classical solution to the corresponding Hamilton-Jacobi-Bellman (HJB) equation. We study the optimal control policy and its properties. The interrelation between the parameters of the model plays a crucial role in the qualitative behavior of the optimal policy. For example, for some ratios between a and b, quite unusual and at first ostensibly counterintuitive policies may appear, like short-selling a stock with a higher rate of return to earn lower interest, or borrowing at a higher rate to invest in a stock with lower rate of return. This is in sharp contrast with the unrestricted case, first studied in Hipp and Plum, or with the case of no short-selling and no borrowing studied in Azcue and Muler.     

The Efficient Use of Conditioning Information in Portfolios

We study the properties of unconditional minimum-variance portfolios in the presence of conditioning information. Such portfolios attain the smallest variance for a given mean among all possible portfolios formed using the conditioning information. We provide explicit solutions for n risky assets, either with or without a riskless asset. Our solutions provide insights into portfolio management problems and issues in conditional asset pricing.     

Safety Transformation and the Structure of the Financial System

This paper studies how a financial system that is organized to efficiently create safe assets responds to macroeconomic shocks. Financial intermediaries face a cost of bearing risk, so they choose the least risky portfolio that backs their issuance of riskless deposits: a diversified pool of nonfinancial firms' debt. Nonfinancial firms choose their capital structure to exploit the resulting segmentation between debt and equity markets. Increased safe asset demand yields larger and riskier intermediaries and more levered firms. Quantitative easing reduces the size and riskiness of intermediaries and can decrease firm leverage, despite reducing borrowing costs at the zero lower bound.     

Risky asset pricing based on safety first fund management

We study a portfolio selection model based on Kataoka's safety-first criterion (KSF model in short). We assume that the market is complete but without risk-free asset, and that the returns are jointly elliptically distributed. With these assumptions, we provide an explicit analytical optimal solution for the KSF model and obtain some geometrical properties of the efficient frontier in the plane of probability risk degree z _α and target return r _α. We further prove a two-fund separation and tangency portfolio theorem in the spirit of the traditional mean-variance analysis. We also establish a risky asset pricing model based on risky funds that is similar to Black's zero-beta capital asset pricing model (CAPM, for short). Moreover, we simplify our risky asset pricing model using a derivative risky fund as a reference for market evaluation.     

Sources of Entropy in Representative Agent Models

We propose two data‐based performance measures for asset pricing models and apply them to models with recursive utility and habits. Excess returns on risky securities are reflected in the pricing kernel's dispersion and riskless bond yields are reflected in its dynamics. We measure dispersion with entropy and dynamics with horizon dependence, the difference between entropy over several periods and one. We compare their magnitudes to estimates derived from asset returns. This exercise reveals tension between a model's ability to generate one‐period entropy, which should be large, and horizon dependence, which should be small.