A Stochastic Extension of the Miller-Modigliani Framework1

This paper deals with the problem of the financial valuation of a firm and its shares of stock with general financing policies in a partial equilibrium framework. the model assumes a time-dependent discount rate and a general stochastic environment in a discrete-time setting. the fundamental valuation approach under the assumption of risk neutrality is used to obtain the time path of share price, the number of outstanding shares, and the value of the firm. These are shown to be the unique conditional expectations of certain stochastic processes. A broad class of firms for which the solution formula yields finite-valued solutions is characterized. the results are extended to the non-risk-neutral case. A regularity condition, which is both necessary and sufficient for the share price to equal the capitalization of future dividends accruing to the share, is obtained. As a mathematical aside, it is shown in the appendix that in the absence of this condition, the so-called stream of dividends approach is meaningless in the sense that it does not yield any financial valuation.     

Hedging and Portfolio Optimization in Financial Markets with a Large Trader

We introduce a general continuous-time model for an illiquid financial market where the trades of a single large investor can move market prices. The model is specified in terms of parameter-dependent semimartingales, and its mathematical analysis relies on the nonlinear integration theory of such semimartingale families. The Itô–Wentzell formula is used to prove absence of arbitrage for the large investor, and, using approximation results for stochastic integrals, we characterize the set of approximately attainable claims. We furthermore show how to compute superreplication prices and discuss the large investor's utility maximization problem.     

PORTFOLIO OPTIMIZATION WITH JUMPS AND UNOBSERVABLE INTENSITY PROCESS

We consider a financial market with one bond and one stock. The dynamics of the stock price process allow jumps which occur according to a Markov-modulated Poisson process. We assume that there is an investor who is only able to observe the stock price process and not the driving Markov chain. The investor's aim is to maximize the expected utility of terminal wealth. Using a classical result from filter theory it is possible to reduce this problem with partial observation to one with complete observation. With the help of a generalized Hamilton–Jacobi–Bellman equation where we replace the derivative by Clarke's generalized gradient, we identify an optimal portfolio strategy. Finally, we discuss some special cases of this model and prove several properties of the optimal portfolio strategy. In particular, we derive bounds and discuss the influence of uncertainty on the optimal portfolio strategy.     

EXPLICIT SOLUTIONS OF CONSUMPTION-INVESTMENT PROBLEMS IN FINANCIAL MARKETS WITH REGIME SWITCHING

We consider a consumption and investment problem where the market presents different regimes. An investor taking decisions continuously in time selects a consumption–investment policy to maximize his expected total discounted utility of consumption. The market coefficients and the investor's utility of consumption are dependent on the regime of the financial market, which is modeled by an observable finite-state continuous-time Markov chain. We obtain explicit optimal consumption and investment policies for specific HARA utility functions. We show that the optimal policy depends on the regime. We also make an economic analysis of the solutions, and show that for every investor the optimal proportion to allocate in the risky asset is greater in a "bull market" than in a "bear market." This behavior is not affected by the investor's risk preferences. On the other hand, the optimal consumption to wealth ratio depends not only on the regime, but also on the investor's risk tolerance: high risk-averse investors will consume relatively more in a "bull market" than in a "bear market," and the opposite is true for low risk-averse investors.     

基金资产管理中的信号传递规律

建立了一种离散状态的信号传递模型,在该模型中,投资人首先聘用一位能力未知的基金经理来管理其资产,然后根据资产收益来修正他的信念。分析在稳健模式和激进模式下投资人关于基金经理能力信念的动态转移规律,决定两种模式优劣的条件。     

Equilibrium Pricing in the Presence of Cumulative Dividends Following a Diffusion

The paper presents some security market pricing results in the setting of a security market equilibrium in continuous time. The theme of the paper is financial valuation theory when the primitive assets pay out real dividends represented by processes of unbounded variation. In continuous time, when the models are also continuous, this is the most general representation of real dividends, and it can be of practical interest to analyze such models.
Taking as the starting point an extension to continuous time of the Lucas consumption-based model, we derive the equilibrium short-term interest rate, present a new derivation of the consumption-based capital asset pricing model, demonstrate how equilibrium forward and futures prices can be derived, including several examples, and finally we derive the equilibrium price of a European call option in a situation where the underlying asset pays dividends according to an Itô process of unbounded variation. In the latter case we demonstrate how this pricing formula simplifies to known results in special cases, among them the famous Black–Scholes formula and the Merton formula for a special dividend rate process.     

相对财富与股票溢价之谜

Mehra和Prescott( 1 985 )提出著名的股票溢价之谜 (EquityPremiumPuzzle) :合理的相对风险规避系数 ,不能解释美国S&P5 0 0指数的收益率为什么比无风险债券的收益率高出 6个百分点。本文提出了一个基于相对财富的资产定价模型 ,其中代表性投资者的效用函数不但依赖于消费 ,还依赖于投资者的绝对财富 ,及社会平均财富。本文使用该模型 ,解释了股票溢价之谜。     

浅析企业财务管理目标

目前流行的企业财务管理目标主要有“股东财富最大化”、“企业价值最大化”两种。从美日模式比较看,我国目前的情况更接近于日本模式,应选择“企业价值最大化”作为理财目标。从契约论角度看,“企业价值最大化”目标可以满足各利益相关者的要求。由于理财目标具有层次性,在实践中,以“企业价值最大化”为总目标,将“现金流量最大化”作为具体目标。     

Are Digital Menus Really Better than Traditional Menus? The Mediating Role of Consumption Visions and Menu Enjoyment

This study examined consumers’ responses to interactive media in a restaurant setting (i.e., digital menus). Study 1 tested a conceptual model, which examined the underlying process shaping customers’ evaluations of a Web-based digital menu. The results demonstrated that consumption visions and menu enjoyment mediated the effects of perceived interactivity on attitudes toward the digital menus. Study 1 also identified direct product experience as an important moderator of the relationship. Study 2 extended and replicated Study 1 in an offline setting by conducting a lab experiment that compared the use of digital and traditional menus in ordering foods that participants have experienced versus those they have not. In general, tablet-based digital menus generated greater enjoyment, increased intentions to adopt, and encouraged participants to order more within a shorter time. But they were preferred only for less-experienced foods. Furthermore, consumption visions were important mediators of interactivity effects in the digital menu condition, but not in the traditional paper menu condition, while menu enjoyment played a mediating role in both conditions.     

A martingale representation theorem and valuation of defaultable securities

We consider a financial framework with two levels of information: the public information generated by the financial assets, and a larger flow of information that contains additional knowledge about a random time. This random time can represent many economic and financial settings, such as the default time of a firm for credit risk, and the death time of an insured for life insurance. As the random time cannot be seen before its occurrence, the progressive enlargement of filtration seems tailor‐fit to model the larger flow of information that incorporates both the public flow and the information about the random time. In this context, our interest focuses on the following challenges: (a) How to single out the various risks coming from the financial assets, the random time, and their correlations? (b) How these risks interplay and lead to the formation of any risk in the larger flow of information? It is clear that understanding how risks build‐up and interact, when one enlarges the flow of information, is vital for an efficient risk management and derivatives' evaluation in those informational markets. Our answers to these challenges are full and complete no matter what the model for the random time is and no matter how the random time is related to the public flow. In fact, we introduce “pure default” risks, and quantify and classify these risks afterward. Then we elaborate our martingale representation results, which state that any martingale in the large filtration stopped at the random time can be decomposed into orthogonal local martingales (i.e., local martingales whose product remains a local martingale). This constitutes our first principal contribution, while our second contribution consists in evaluating various defaultable securities according to the recovery policy, within our financial setting that encompasses any default model, using a martingale “basis.” Our pricing formulas explain the impact of various recovery policies on securities and determine the types of pure default risk they entail.     

如何在金融市场中进行资产配置

在金融市场中进行资产配置关键是合理估算资产的相关风险和收益情形,根据投资者状况构建有效的资产配置模型。研究资产配置的基础知识,并就风险度量的方法进行比较分析;考察投资者个人状况,分别针对一般理性投资者和悲观投资者,构建一般资产配置模型和极大极小模型。     

MAXIMUM LIKELIHOOD ESTIMATION USING PRICE DATA OF THE DERIVATIVE CONTRACT

This article develops a general methodology that uses the observed prices of a derivative contract to compute maximum likelihood parameter estimates for an unobserved asset value process. the use of this estimation methodology is demonstrated in two applications: Vasicek's term structure model and deposit insurance pricing. This methodology can also be useful in the empirical analysis of complex financial contracts involving embedded options.     

Semi‐efficient valuations and put‐call parity

We propose an approach to the valuation of payoffs in general semimartingale models of financial markets where prices are nonnegative. Each asset price can hit 0; we only exclude that this ever happens simultaneously for all assets. We start from two simple, economically motivated axioms, namely, absence of arbitrage (in the sense of NUPBR) and absence of relative arbitrage among all buy‐and‐hold strategies (called static efficiency). A valuation process for a payoff is then called semi‐efficient consistent if the financial market enlarged by that process still satisfies this combination of properties. It turns out that this approach lies in the middle between the extremes of valuing by risk‐neutral expectation and valuing by absence of arbitrage alone. We show that this always yields put‐call parity, although put and call values themselves can be nonunique, even for complete markets. We provide general formulas for put and call values in complete markets and show that these are symmetric and that both contain three terms in general. We also show that our approach recovers all the put‐call parity respecting valuation formulas in the classic theory as special cases, and we explain when and how the different terms in the put and call valuation formulas disappear or simplify. Along the way, we also define and characterize completeness for general semimartingale financial markets and connect this to the classic theory.     

A multiobjective financial planning model for electric utility rate regulation

The interests of the three parties to the regulatory process—investors in an electric utility, consumers, and regulators—are often in conflict. Investors are concerned with shareholder wealth maximization, while consumers desire dependable service at low rates. If the desired end product of regulation is to establish rates that balance the interests of consumers and investors, then a financial planning model is needed that accurately reflects the multi-objective nature of the regulatory decision process. This article develops such a multi-objective programming model for examining the efficient trade-offs available to utility regulators in setting rates of return.     

INCOMPLETE MARKETS IN INFINITE HORIZON: DEBT CONSTRAINTS VERSUS NODE PRICES1

The general equilibrium model with incomplete markets is here extended to infinite horizon economies populated by a finite number of infinitely lived agents. the crucial issue that divides the infinite horizon setting from the finite horizon setting is in the nature of borrowing constraints, which added to spot constraints, define a plausible budget set for individual agents. the paper relates seven alternative definitions of equilibrium and states corresponding equilibrium existence theorems when assets are one-period and purely financial.     

MULTIFRACTIONAL STOCHASTIC VOLATILITY MODELS

The aim of this work is to advocate the use of multifractional Brownian motion (mBm) as a relevant model in financial mathematics. mBm is an extension of fractional Brownian motion where the Hurst parameter is allowed to vary in time. This enables the possibility to accommodate for varying local regularity, and to decouple it from long‐range dependence properties. While we believe that mBm is potentially useful in a variety of applications in finance, we focus here on a multifractional stochastic volatility Hull & White model that is an extension of the model studied in Comte and Renault. Using the stochastic calculus with respect to mBm developed in Lebovits and Lévy Véhel, we solve the corresponding stochastic differential equations. Since the solutions are of course not explicit, we take advantage of recently developed numerical techniques, namely functional quantization‐based cubature methods, to get accurate approximations. This allows us to test the behavior of our model (as well as the one in Comte and Renault) with respect to its parameters, and in particular its ability to explain some features of the implied volatility surface. An advantage of our model is that it is able both to fit smiles at different maturities, and to take volatility persistence into account in a more precise way than Comte and Renault.     

The financialization of the non‐financial corporation. A critique to the financial turn of accumulation hypothesis

One aspect in which non‐financial corporations (NFCs) are said to be financialized is that they have been increasingly engaged in financial accumulation from which they derive a growing proportion of financial income. This is what we call the financial turn of accumulation hypothesis. In this article, we show that the evidence used to sustain it, in the U.S. setting, has to be reconsidered. Our findings show that, contrary to the financial turn of accumulation hypothesis, financial income averages 2.5% of NFCs’ total income since the 1980s, oscillating since the beginnings of the 1990s until 2005 and then declining. In terms of assets, some of the alleged financial assets might actually reflect other activities in which NFCs have been increasingly engaged, such as tax avoidance, internationalization of production, activities refocusing and M&As.     

Optimal equilibria for time‐inconsistent stopping problems in continuous time

For an infinite‐horizon continuous‐time optimal stopping problem under nonexponential discounting, we look for an optimal equilibrium, which generates larger values than any other equilibrium does on the entire state space. When the discount function is log subadditive and the state process is one‐dimensional, an optimal equilibrium is constructed in a specific form, under appropriate regularity and integrability conditions. Although there may exist other optimal equilibria, we show that they can differ from the constructed one in very limited ways. This leads to a sufficient condition for the uniqueness of optimal equilibria, up to some closedness condition. To illustrate our theoretic results, a comprehensive analysis is carried out for three specific stopping problems, concerning asset liquidation and real options valuation. For each one of them, an optimal equilibrium is characterized through an explicit formula.     

CONSUMPTION AND PORTFOLIO POLICIES WITH INCOMPLETE MARKETS AND SHORT-SALE CONSTRAINTS IN THE FINITE-DIMENSIONAL CASE: SOME REMARKS

This paper extends He and Pearson's (1991) martingale approach to the study of optimal intertemporal consumption and portfolio policies with incomplete markets and short-sale constraints to a framework in which no assumptions are made on the price process for the securities. We show how both their characterization of the budget-feasible set and duality result can be extended to account for an unbounded set II of Arrow-Debreu state prices compatible with the arbitrage-free assumption. We also supply a (fairly general) sufficient condition for II to be bounded, as required in their setting.     

ASSET ALLOCATION AND ANNUITY-PURCHASE STRATEGIES TO MINIMIZE THE PROBABILITY OF FINANCIAL RUIN

In this paper, we derive the optimal investment and annuitization strategies for a retiree whose objective is to minimize the probability of lifetime ruin, namely the probability that a fixed consumption strategy will lead to zero wealth while the individual is still alive. Recent papers in the insurance economics literature have examined utility-maximizing annuitization strategies. Others in the probability, finance, and risk management literature have derived shortfall-minimizing investment and hedging strategies given a limited amount of initial capital. This paper brings the two strands of research together. Our model pre-supposes a retiree who does not currently have sufficient wealth to purchase a life annuity that will yield her exogenously desired fixed consumption level. She seeks the asset allocation and annuitization strategy that will minimize the probability of lifetime ruin. We demonstrate that because of the binary nature of the investor's goal, she will not annuitize any of her wealth until she can fully cover her desired consumption with a life annuity. We derive a variational inequality that governs the ruin probability and the optimal strategies, and we demonstrate that the problem can be recast as a related optimal stopping problem which yields a free-boundary problem that is more tractable. We numerically calculate the ruin probability and optimal strategies and examine how they change as we vary the mortality assumption and parameters of the financial model. Moreover, for the special case of exponential future lifetime, we solve the (dual) problem explicitly. As a byproduct of our calculations, we are able to quantify the reduction in lifetime ruin probability that comes from being able to manage the investment portfolio dynamically and purchase annuities.