RISK MEASURES ON ORLICZ HEARTS

Coherent, convex, and monetary risk measures were introduced in a setup where uncertain outcomes are modeled by bounded random variables. In this paper, we study such risk measures on Orlicz hearts. This includes coherent, convex, and monetary risk measures on L^p -spaces for  1 ≤ p < ∞  and covers a wide range of interesting examples. Moreover, it allows for an elegant duality theory. We prove that every coherent or convex monetary risk measure on an Orlicz heart which is real-valued on a set with non-empty algebraic interior is real-valued on the whole space and admits a robust representation as maximal penalized expectation with respect to different probability measures. We also show that penalty functions of such risk measures have to satisfy a certain growth condition and that our risk measures are Luxemburg-norm Lipschitz-continuous in the coherent case and locally Luxemburg-norm Lipschitz-continuous in the convex monetary case. In the second part of the paper we investigate cash-additive hulls of transformed Luxemburg-norms and expected transformed losses. They provide two general classes of coherent and convex monetary risk measures that include many of the currently known examples as special cases. Explicit formulas for their robust representations and the maximizing probability measures are given.     

Model risk in credit risk

We provide sharp analytical upper and lower bounds for value‐at‐risk (VaR) and sharp bounds for expected shortfall (ES) of portfolios of any dimension subject to default risk. To do so, the main methodological contribution of the paper consists in analytically finding the convex hull generators for the class of exchangeable Bernoulli variables with given mean and for the class of exchangeable Bernoulli variables with given mean and correlation in any dimension. Using these analytical results, we first describe all possible dependence structures for default, in the class of finite sequences of exchangeable Bernoulli random variables. We then measure how model risk affects VaR and ES.     

MARKOWITZ'S PORTFOLIO OPTIMIZATION IN AN INCOMPLETE MARKET

In this paper, for a process S , we establish a duality relation between K_p , the     - closure of the space of claims in     , which are attainable by "simple" strategies, and     , all signed martingale measures     with     , where   p ≥ 1, q ≥ 1  and     . If there exists a     with     a.s., then K_p consists precisely of the random variables     such that ϑ is predictable S -integrable and     for all     . The duality relation corresponding to the case   p = q = 2  is used to investigate the Markowitz's problem of mean–variance portfolio optimization in an incomplete market of semimartingale model via martingale/convex duality method. The duality relationship between the mean–variance efficient portfolios and the variance-optimal signed martingale measure (VSMM) is established. It turns out that the so-called market price of risk is just the standard deviation of the VSMM. An illustrative example of application to a geometric Lévy processes model is also given.     

Put Option Premiums and Coherent Risk Measures

This note defines the premium of a put option on the firm as a measure of insolvency risk. The put premium is not a coherent risk measure as defined by Artzner et al. (1999). It satisfies all the axioms for a coherent risk measure except one, the translation invariance axiom. However, it satisfies a weakened version of the translation invariance axiom that we label translation monotonicity. The put premium risk measure generates an acceptance set that satisfies the regularity Axioms 2.1–2.4 of Artzner et al. (1999). In fact, this is a general result for any risk measure satisfying the same risk measure axioms as the put premium. Finally, the coherent risk measure generated by the put premium's acceptance set is the minimal capital required to protect the firm against insolvency uniformly across all states of nature.     

Epstein-Zin utility maximization on a random horizon

This paper solves the consumption-investment problem under Epstein-Zin preferences on a random horizon. In an incomplete market, we take the random horizon to be a stopping time adapted to the market filtration, generated by all observable, but not necessarily tradable, state processes. Contrary to prior studies, we do not impose any fixed upper bound for the random horizon, allowing for truly unbounded ones. Focusing on the empirically relevant case where the risk aversion and the elasticity of intertemporal substitution are both larger than one, we characterize the optimal consumption and investment strategies using backward stochastic differential equations with superlinear growth on unbounded random horizons. This characterization, compared with the classical fixed-horizon result, involves an additional stochastic process that serves to capture the randomness of the horizon. As demonstrated in two concrete examples, changing from a fixed horizon to a random one drastically alters the optimal strategies.     

Mean Reversion and the Comovement of Equilibrium Spot and Futures Prices: Implications from Alternative Data‐Generating Processes

The comovements of spot and futures prices are characterized by six binary variables, including the term structure curvature of futures prices. These variables are used to uniquely identify 48 possible comovement patterns. Among them, 24 cases are associated with mean reversion, which is defined as a state when spreads between futures and spot prices are shrinking. These pattern frequencies are then calculated on a daily basis with the futures prices of 10 commodities, including precious metal, agricultural, and financial commodities. The results are further compared to simulation output from three data‐generating processes: a bivariate pure random walk, a mixed random walk with first‐order autoregression (AR(1)), and an error‐correction representation. The mean‐reverting frequencies for all 10 commodities are about 50%. Around half of the time, spot and futures prices are moving toward each other, and the rest of the time they move in the same direction. The symmetry of these results implies that the existence of substantial shocks originated from futures markets; thus, this is consistent with the risk premium view of futures trading. Also, although all simulation models produce similar mean‐reversion frequencies, the patterns of comovements of spot and futures prices are different, and the price dynamics depend heavily on whether the market is dominant contango or backwardation. Furthermore, the error‐correction model outperforms the random‐walk model for agricultural commodities, and the mixed random walk with AR(1) is hardly distinguishable from the pure random walk. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:769–796, 2001     

TOPSIS Based Approach to Scoring Negotiating Offers in Negotiation Support Systems

In this paper we analyze the possibility of applying the technique for order preferences by similarity to ideal solution (TOPSIS) to building the scoring system for negotiating offers. TOPSIS is a multiple criteria decision making method that is based on measuring distances between alternatives under consideration and two bipolar reference alternatives, a positive and negative ideal. Thus the criteria used for the evaluation of alternatives should be described using strong scales. However, in the negotiation, the issues are very often described qualitatively, which results in ordinal or even nominal variables that must be taken into consideration in offers’ evaluation process. What is more, TOPSIS may be applied to solving the discrete decision problems while the negotiation space may be defined by the means of continuous variables too. In this paper we try to modify the TOPSIS algorithm to make it applicable to negotiation support and, moreover, discuss the following methodological issues: using TOPSIS for a negotiation problem with continuous negotiation space; selecting the distance measure for adequate representation of negotiator’s preferences and measuring distances for qualitative issues. Finally, we propose a simple additional mechanism that allows for building the TOPSIS-based scoring system for negotiating offers and does not involve negotiators in time consuming and tiresome preference elicitation process. This mechanism requires from negotiators to construct examples of offers that represent some categories of quality and then by using a goal programming approach it infers all the parameters required by the TOPSIS algorithm. We also show a simple prototype software tool that applies the TOPSIS modified algorithm and may be used in electronic negotiation support.     

When Do Long‐term Imbalances Lead to Current Account Reversals?

We extend the literature on sharp reductions in current account deficits by taking into account not only short‐term determinants, but also the deviation of net foreign assets from their long‐run equilibrium level. First, we analyse the long‐term relationship between net foreign assets and a set of explanatory variables and construct a measure of imbalances. Next, we model current account reversals by incorporating this new measure and compare the predictive power of this model with the baseline specification that does not account for long‐term imbalances. Our new model has a superior performance in and out‐of‐sample, especially when we control for the sign of imbalances. We also find that low net foreign assets do not necessarily lead to sharp reductions in current account deficits; it is rather the situation when they are below their equilibrium level that triggers reversals. Finally, we document that our new measure of net foreign asset imbalances is important only for developing countries, whereas standard models perform well for industrial economies.     

MULTIVARIATE RISK MEASURES: A CONSTRUCTIVE APPROACH BASED ON SELECTIONS

Since risky positions in multivariate portfolios can be offset by various choices of capital requirements that depend on the exchange rules and related transaction costs, it is natural to assume that the risk measures of random vectors are set‐valued. Furthermore, it is reasonable to include the exchange rules in the argument of the risk measure and so consider risk measures of set‐valued portfolios. This situation includes the classical Kabanov's transaction costs model, where the set‐valued portfolio is given by the sum of a random vector and an exchange cone, but also a number of further cases of additional liquidity constraints. We suggest a definition of the risk measure based on calling a set‐valued portfolio acceptable if it possesses a selection with all individually acceptable marginals. The obtained selection risk measure is coherent (or convex), law invariant, and has values being upper convex closed sets. We describe the dual representation of the selection risk measure and suggest efficient ways of approximating it from below and from above. In the case of Kabanov's exchange cone model, it is shown how the selection risk measure relates to the set‐valued risk measures considered by Kulikov (2008, Theory Probab. Appl. 52, 614–635), Hamel and Heyde (2010, SIAM J. Financ. Math. 1, 66–95), and Hamel, Heyde, and Rudloff (2013, Math. Financ. Econ. 5, 1–28).     

从购买风险感知理论解释商业集聚对店铺印象的影响

商业集聚印象必然会影响集聚中的店铺印象,这个现象可以用购买风险感知理论进行解释。文章将消费者购买风险感知引入店铺印象转移模型中,从消费者心理的角度,探查商业集聚印象对店铺印象的影响原因,通过比较消费者在不同背景下购买心理的变化,揭示店铺印象转移产生的本源。结论得出:购物风险感知在百货店印象转移中起调节作用,在专业店印象转移中起中介作用。     

Toward understanding business student professional development engagement

Professional development engagement (PDE) is defined as the level of perceived undergraduate engagement in professional development activities. An 11-item measure of PDE exhibited a good reliability. Using a complete data sample of 467 graduating business undergraduates, four variable sets (student background or precollege variables, college-related variables, organization-related variables, and motivation-related variables) each explained significant incremental variance in PDE. Significant individual correlates of PDE included joining a student professional organization and motivation to attend business school. One outcome suggests that business schools need to leverage technology more aggressively to deliver professional development content both asynchronously and synchronously to more of their undergraduates.     

Convergence of utility indifference prices to the superreplication price in a multiple‐priors framework

This paper formulates a utility indifference pricing model for investors trading in a discrete time financial market under nondominated model uncertainty. Investor preferences are described by possibly random utility functions defined on the positive axis. We prove that when the investors's absolute risk aversion tends to infinity, the multiple‐priors utility indifference prices of a contingent claim converge to its multiple‐priors superreplication price. We also revisit the notion of certainty equivalent for multiple‐priors and establish its relation with risk aversion.     

DYNAMIC INDIFFERENCE VALUATION VIA CONVEX RISK MEASURES

The (subjective) indifference value of a payoff in an incomplete financial market is that monetary amount which leaves an agent indifferent between buying or not buying the payoff when she always optimally exploits her trading opportunities. We study these values over time when they are defined with respect to a dynamic monetary concave utility functional, that is, minus a dynamic convex risk measure. For that purpose, we prove some new results about families of conditional convex risk measures. We study the convolution of abstract conditional convex risk measures and show that it preserves the dynamic property of time-consistency. Moreover, we construct a dynamic risk measure (or utility functional) associated to superreplication in a market with trading constraints and prove that it is time-consistent. By combining these results, we deduce that the corresponding indifference valuation functional is again time-consistent. As an auxiliary tool, we establish a variant of the representation theorem for conditional convex risk measures in terms of equivalent probability measures.     

The Effect of CEO Risk Appetite on Firm Volatility: An Empirical Analysis of Financial Firms☆

This paper examines the effect of CEO risk appetite on the return volatility of a sample of large, listed financial firms over the period 2000–2008. After controlling for firm specific characteristics, the results give strong evidence that the CEO risk appetite has an important effect on firm volatility. The biographical measures for CEO risk appetite are significant explanatory variables of all measures of firm volatility employed in this study. The effect of CEO age is significant and positive for all four volatility measures, while CEO education and current job tenure are negative and significant for all four measures. Executive experience with other firm boards has a negative and significant effect on total and idiosyncratic volatility. Interestingly, CEO wealth is complementary to the other biographical variables with a positive effect on all but the default volatility measure. Our results carry implications for shareholders, financial regulators, governments, and managers.     

Portfolio Optimization and Martingale Measures

The paper studies connections between risk aversion and martingale measures in a discrete-time incomplete financial market. An investor is considered whose attitude toward risk is specified in terms of the index b of constant proportional risk aversion. Then dynamic portfolios are admissible if the terminal wealth is positive. It is assumed that the return (risk) processes are bounded. Sufficient (and nearly necessary) conditions are given for the existence of an optimal dynamic portfolio which chooses portfolios from the interior of the set of admissible portfolios. This property leads to an equivalent martingale measure defined through the optimal dynamic portfolio and the index 0 < b ≤ 1. Moreover, the option pricing formula of Davis is given by this martingale measure. In the case of b = 1; that is, in the case of the log-utility, the optimal dynamic portfolio defines the numéraire portfolio.     

Does innovativeness reduce startup survival rates?

There are two competing hypotheses explaining how innovativeness influences the survival of startups: On the one hand, innovativeness is argued to foster survival-enhancing attributes (e.g., market power and cost efficiency) and capabilities (e.g., absorptive capacity). On the other hand, an innovative startup faces (and bears the associated risks of) liabilities of newness and smallness that exceed those of its non-innovative counterparts. The available empirical literature addressing this theoretical tension mostly supports the former hypothesis; we suggest that this finding is, in part, driven by the common practice of employing an ex post measure that already embodies a degree of success in innovativeness. We use an ex ante measure and find that a startup's innovativeness is negatively associated with its subsequent survival. We also find that entrepreneurs' greater appetite for risk magnifies this negative association. These findings imply that pursuing innovations is not necessarily associated with survival during the early stages of firm development and entails a more complicated start-up process.     

Asymmetric Correlations in Predicting Portfolio Returns*

Rigorous statistical tests have been designed to detect the existence of asymmetric correlations. However, these tests can hardly further facilitate future investment or risk management because asymmetric correlations are time‐varying and difficult to predict. In this paper, we construct a unified state‐space model, which not only measures in‐sample asymmetric correlations, but also exploit out‐of‐sample asymmetric correlations in the context of predicting portfolio returns. First, we regard time‐varying correlation between market returns and portfolio returns as a state variable and model it as an AR(1) process. Then, we measure future asymmetric correlations based on correlation coefficients between two unpredictable components in market returns and correlation, respectively. Third, we clarify the intuition, calculate asymmetric correlations for two portfolio sets and estimate the economic value of applying our model in asset allocation. Finally, we try to search for potential variables that can explain future asymmetric correlations. The results show that market‐wide liquidity, variance, earning price ratio, and investor sentiment can partially explain the asymmetry correlation phenomenon.     

不良资产证券化资产池信用风险测算研究——基于神经网络

不良资产证券化资产池信用风险的定量研究在我国非常匮乏.文章立足我国不良资产信用数据严重不足的现状,尝试使用改进的BP神经网络模型测算单笔不良资产的信用风险:根据不良资产的特点甄选出其中16个作为输入变量;经过反复测试,确定1个隐含层;以单笔资产的信用风险作为输出层.然后通过整合信用风险附加模型,量化资产池的信用风险.通过对我国某不良资产证券化案例为样本进行的实证分析结果表明,基于改进的BP神经网络模型测算资产池信用风险具有良好的应用效果.     

EXACT SOLUTION OF A MARTINGALE STOCHASTIC VOLATILITY OPTION PROBLEM AND ITS EMPIRICAL EVALUATION

Exact explicit solution of the log-normal stochastic volatility (SV) option model has remained an open problem for two decades. In this paper, I consider the case where the risk-neutral measure induces a martingale volatility process, and derive an exact explicit solution to this unsolved problem which is also free from any inverse transforms. A representation of the asset price shows that its distribution depends on that of two random variables, the terminal SV as well as the time average of future stochastic variances. Probabilistic methods, using the author's previous results on stochastic time changes, and a Laplace–Girsanov Transform technique are applied to produce exact explicit probability distributions and option price formula. The formulae reveal interesting interplay of forces between the two random variables through the correlation coefficient. When the correlation is set to zero, the first random variable is eliminated and the option formula gives the exact formula for the limit of the Taylor series in Hull and White's (1987) approximation. The SV futures option model, comparative statics, price comparisons, the Greeks and practical and empirical implementation and evaluation results are also presented. A PC application was developed to fit the SV models to current market prices, and calculate other option prices, and their Greeks and implied volatilities (IVs) based on the results of this paper. This paper also provides a solution to the option implied volatility problem, as the empirical studies show that, the SV model can reproduce market prices, better than Black–Scholes and Black-76 by up to 2918%, and its IV curve can reproduce that of market prices very closely, by up to within its 0.37%.     

CHOQUET PRICING FOR FINANCIAL MARKETS WITH FRICTIONS1

In markets where dealers play a central role, bid-ask spreads inhibit asset valuation as defined by the formation cost of a replicating portfolio. We introduce a nonlinear valuation formula similar to the usual expectation with respect to the risk-adjusted probability measure. This formula expresses the asset's selling and buying prices set by dealers as the Choquet integrals of their random payoffs We investigate several price puzzles: the violation of the put-call parity and the fact that the components of a security can sell at a premium to the underlying security (primes and scores).