Optional decomposition and Lagrange multipliers

Let be the set of equivalent martingale measures for a given process , and let be a process which is a local supermartingale with respect to any measure in . The optional decomposition theorem for states that there exists a predictable integrand such that the difference is a decreasing process. In this paper we give a new proof which uses techniques from stochastic calculus rather than functional analysis, and which removes any boundedness assumption.     

从制度经济学角度分析土地流转

我国农村土地制度具有三个特点:等级性、社区封闭性和政府控制。与产权残缺相比,土地的保障功能更可能是减少供给从而阻碍土地流转的主要原因。土地承包权只有成为物权,才能表现为一种具有交换价值的独立资产。赋予农户以处分权的意义也在于使承包者能够将承包权当作独立的交换价值进行流转。只有存在完整意义上的承包经营权,才谈得上形成土地使用权流转的市场机制。     

Optimal consumption and investment with Epstein–Zin recursive utility

We study continuous-time optimal consumption and investment with Epstein–Zin recursive preferences in incomplete markets. We develop a novel approach that rigorously constructs the solution of the associated Hamilton–Jacobi–Bellman equation by a fixed point argument and makes it possible to compute both the indirect utility and, more importantly, optimal strategies. Based on these results, we also establish a fast and accurate method for numerical computations. Our setting is not restricted to affine asset price dynamics; we only require boundedness of the underlying model coefficients.     

On the integrability of money-demand functions by the Sidrauski and the shopping-time models

This paper investigates which properties money-demand functions must satisfy so that they are consistent with Lucas’s [Lucas Jr., R.E., 2000. Inflation and welfare. Econometrica 68, 247–274] versions of the Sidrauski and the shopping-time models. We conclude that shopping-time-integrable money-demand functions are necessarily also Sidrauski-integrable, but that the converse is not necessarily true, unless a boundedness assumption on the nominal interest rate is made. Both the log–log with an interest-rate elasticity greater than or equal to one and the semi-log money demands may serve as counterexamples. All the models and results are also extended to the case in which there are several assets in the economy performing monetary functions.     

q-Optimal Martingale Measures for Discrete Time Models

We focus on a backward induction of the q-optimal martingale measure for discrete-time models, where 1  <  q  <  ∞. As for the bounded asset price process case, the same backward induction has been obtained by Grandits (Bernoulli, 5:225–247, 1999). To remove the boundedness, we shall discuss a sufficient condition under which there exists a signed martingale measure whose density is in the ${\mathcal {L}^q}$ -space, which topic is our second aim.     

The numéraire portfolio in semimartingale financial models

We study the existence of the numéraire portfolio under predictable convex constraints in a general semimartingale model of a financial market. The numéraire portfolio generates a wealth process, with respect to which the relative wealth processes of all other portfolios are supermartingales. Necessary and sufficient conditions for the existence of the numéraire portfolio are obtained in terms of the triplet of predictable characteristics of the asset price process. This characterization is then used to obtain further necessary and sufficient conditions, in terms of a no-free-lunch-type notion. In particular, the full strength of the “No Free Lunch with Vanishing Risk” (NFLVR) condition is not needed, only the weaker “No Unbounded Profit with Bounded Risk” (NUPBR) condition that involves the boundedness in probability of the terminal values of wealth processes. We show that this notion is the minimal a-priori assumption required in order to proceed with utility optimization. The fact that it is expressed entirely in terms of predictable characteristics makes it easy to check, something that the stronger NFLVR condition lacks.      

Book Review

This paper investigates the role of intellectual capital information (ICI) in sell-side analysts’ fundamental analysis and valuation of companies. Using in-depth semi-structured interviews, it penetrates the black box of analysts’ valuation decision-making by identifying and conceptualising the mechanisms and rationales by which ICI is integrated within their valuation decision processes. We find that capital market participants are not ambivalent to ICI, and ICI is used: (1) to form analysts’ perceptions of the overall quality, strengths and future prospects of companies; (2) in deriving valuation model inputs; (3) in setting price targets and making investment recommendations; and (4) as an important and integral element in analyst–client communications. We show that: there is a ‘pecking order’ of mechanisms for incorporating ICI in valuations, based on quantifiability; IC valuation is grounded in valuation theory; there are designated entry points in the valuation process for ICI; and a number of factors affect analysts’ ICI use in valuation. We also identify a need to redefine ‘value-relevant’ ICI to include non-price-sensitive information; acknowledge the boundedness and contextuality of analysts’ rationality and motives of their ICI use; and the important role of analyst–client meetings for ICI communication.     

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.     

Numerical solutions to an integro-differential parabolic problem arising in the pricing of financial options in a Levy market

We study the numerical solutions for an integro-differential parabolic problem modeling a process with jumps and stochastic volatility in financial mathematics. We present two general algorithms to calculate numerical solutions. The algorithms are implemented in PDE2D, a general-purpose, partial differential equation solver.