Sharing the value‐at‐risk under distributional ambiguity

This paper considers the problem of risk sharing, where a coalition of homogeneous agents, each bearing a random cost, aggregates their costs, and shares the value‐at‐risk of such a risky position. Due to limited distributional information in practice, the joint distribution of agents' random costs is difficult to acquire. The coalition, being aware of the distributional ambiguity, thus evaluates the worst‐case value‐at‐risk within a commonly agreed ambiguity set of the possible joint distributions. Through the lens of cooperative game theory, we show that this coalitional worst‐case value‐at‐risk is subadditive for the popular ambiguity sets in the distributionally robust optimization literature that are based on (i) convex moments or (ii) Wasserstein distance to some reference distributions. In addition, we propose easy‐to‐compute core allocation schemes to share the worst‐case value‐at‐risk. Our results can be readily extended to sharing the worst‐case conditional value‐at‐risk under distributional ambiguity.     

Mean‐field games with differing beliefs for algorithmic trading

Even when confronted with the same data, agents often disagree on a model of the real world. Here, we address the question of how interacting heterogeneous agents, who disagree on what model the real world follows, optimize their trading actions. The market has latent factors that drive prices, and agents account for the permanent impact they have on prices. This leads to a large stochastic game, where each agents performance criteria are computed under a different probability measure. We analyze the mean‐field game (MFG) limit of the stochastic game and show that the Nash equilibrium is given by the solution to a nonstandard vector‐valued forward–backward stochastic differential equation. Under some mild assumptions, we construct the solution in terms of expectations of the filtered states. Furthermore, we prove that the MFG strategy forms an ε‐Nash equilibrium for the finite player game. Finally, we present a least square Monte Carlo based algorithm for computing the equilibria and show through simulations that increasing disagreement may increase price volatility and trading activity.     

A STATE‐CONSTRAINED DIFFERENTIAL GAME ARISING IN OPTIMAL PORTFOLIO LIQUIDATION

We consider n risk‐averse agents who compete for liquidity in an Almgren–Chriss market impact model. Mathematically, this situation can be described by a Nash equilibrium for a certain linear quadratic differential game with state constraints. The state constraints enter the problem as terminal boundary conditions for finite and infinite time horizons. We prove existence and uniqueness of Nash equilibria and give closed‐form solutions in some special cases. We also analyze qualitative properties of the equilibrium strategies and provide corresponding financial interpretations.     

Effects of game‐product congruity on in‐app interstitial advertising and the moderation of media‐context factors

Advertising has become one of the major sources of game apps revenues and interstitial ads, in particular, are the most used monetization method among the types of in‐game mobile ad formats. Interstitial ads overlaid on top of a mobile game app have more obvious advertising intent and a higher degree of forced exposure and perceived intrusiveness. This study examined how the degree of congruity (high vs. moderate vs. low) between the promoted products in interstitial ads and the mobile game app environment affects consumers’ responses. The moderating effects of media‐context factors (i.e., excited– or calm–happiness game types and game immersion) were further assessed. The results of two experiments revealed that game‐product congruity lead to better consumers’ responses toward ads and advertised products. The positive effects of game‐product congruity were more salient when consumers played calm–happiness games and were less immersed in the game. Theoretical implications on integrating perspectives across disciplines such as schema theory, happiness, and immersion within the media‐context framework, as well as practical suggestions are discussed.     

Exploring South African consumers’ attitudes towards game meat—Utilizing a multi‐attribute attitude model

The study explored the use of a multi‐attribute approach, Fishbein’s attitude‐towards‐the‐object model, in finding the differences between the attitudes of consumers and nonconsumers of game meat among South African respondents towards the following attributes of game meat: sensory characteristics; health benefits; game meat production ethics; animal welfare; safety for human consumption; availability; and price. This quantitative study determined the attitudes of 1,096 consumers and 310 nonconsumers of game meat with an online survey. Based on attitudes towards individual attributes, as determined by Fishbein’s attitude‐towards‐the‐object model, respondents classified some product attributes as important in their decision to consume, or not to consume, game meat. Respondents indicated that the availability, sensory characteristics, game meat production ethics and health benefits are considered to be important in their decision to consume game meat.     

Arbitrage‐free XVA

We develop a framework for computing the total valuation adjustment (XVA) of a European claim accounting for funding costs, counterparty credit risk, and collateralization. Based on no‐arbitrage arguments, we derive backward stochastic differential equations associated with the replicating portfolios of long and short positions in the claim. This leads to the definition of buyer's and seller's XVA, which in turn identify a no‐arbitrage interval. In the case that borrowing and lending rates coincide, we provide a fully explicit expression for the unique XVA, expressed as a percentage of the price of the traded claim, and for the corresponding replication strategies. In the general case of asymmetric funding, repo, and collateral rates, we study the semilinear partial differential equations characterizing buyer's and seller's XVA and show the existence of a unique classical solution to it. To illustrate our results, we conduct a numerical study demonstrating how funding costs, repo rates, and counterparty risk contribute to determine the total valuation adjustment.     

Explaining autonomy variations across value‐chain activities in foreign‐owned subsidiaries

This article is one of the first to combine the asset bundling model and neo‐configurational perspective to explain autonomy variations across different value‐chain activities in foreign‐owned subsidiaries. We develop tentative answers to three research questions based on survey data of subsidiaries located in Taiwan and Thailand. We use fuzzy set qualitative comparative analysis technique to analyze the data. We found that competence bundles in primary and support activities are key for autonomy development across basic and advanced value‐adding activities. Strong relationships with local business networks are more important for autonomy development than links to universities or governmental institutions. The global city location plays a lesser role than expected and the geographic distance is a hindrance to autonomy development in basic as well as advanced value‐chain activities.     

ARROW–DEBREU EQUILIBRIA FOR RANK‐DEPENDENT UTILITIES

We provide conditions on a one‐period‐two‐date pure exchange economy with rank‐dependent utility agents under which Arrow–Debreu equilibria exist. When such an equilibrium exists, we show that the state‐price density is a weighted marginal rate of intertemporal substitution of a representative agent, where the weight depends on the differential of the probability weighting function. Based on the result, we find that asset prices depend upon agents' subjective beliefs regarding overall consumption growth, and we offer a direction for possible resolution of the equity premium puzzle.     

BILATERAL COUNTERPARTY RISK UNDER FUNDING CONSTRAINTS—PART II: CVA

The correction in value of an over‐the‐counter derivative contract due to counterparty risk under funding constraints is represented as the value of a dividend‐paying option on the value of the contract clean of counterparty risk and excess funding costs. This representation allows one to analyze the structure of this correction, the so‐called Credit Valuation Adjustment (CVA for short), in terms of replacement cost/benefits, credit cost/benefits, and funding cost/benefits. We develop a reduced‐form backward stochastic differential equations (BSDE) approach to the problem of pricing and hedging the CVA. In the Markov setup, explicit CVA pricing and hedging schemes are formulated in terms of semilinear partial differential equations.     

Entrepreneurs as Sophisticated Iconoclasts: Rational Rule‐Breaking in an Experimental Game

We analyzed the theoretical relationship between rule‐breaking by entrepreneurs and realized advantage. We tested the tenets of that relationship using an experiment where subjects, including entrepreneurs, compete in a business strategy game where rule‐breaking is possible (but does not directly correlate with benefits). We found that entrepreneurs break the rules more often and realize greater benefits because they break rules in a smarter way. The ability to be sophisticated in rule‐breaking behavior stems from breaking the rules earlier and responding more aggressively to positive feedback. Such actions can create new net value in the economy—reinforcing the idea of entrepreneurship as a social good.     

Agents with other‐regarding preferences in the commons

We present a unified approach to study the problem of the commons for agents with other‐regarding preferences. This situation is modeled as a game with vector‐valued utilities. Several types of agents are characterized depending on the importance assigned to the components of their utility functions. We obtain the set of equilibria of the game with two types of agents, pro‐social and pro‐self, and some refinements of this set for conservative agents. The most relevant result is that only a pro‐social agent is required to avoid the tragedy of the commons, regardless of the behavior of the rest of the agents.     

Does a money‐is‐all attitude cause alienation? A cross‐cultural comparison of Korea,the US and Sweden

Money is increasingly being attributed more value in society, although a money‐is‐all attitude decreases social relationships and increases alienation in modern, industrialized societies. This research investigated the influence of this money‐is‐all attitude on alienation based on a cross‐cultural comparison of Korea, the US and Sweden. The money‐is‐all attitude was defined as a perspective in which money is regarded as an indicator of achievement or success. Self‐administered online surveys were conducted with consumers ranging between the ages of 20 to 49 in Korea, the US and Sweden. The money‐is‐all attitude and alienation seemed to be more pervasive in Korea than in the US or Sweden. The money‐is‐all attitude was the factor with the strongest influence on alienation when controlling for socio‐demographic factors. Furthermore, participation in sports activities was an important factor in decreasing alienation levels. The findings of this research imply that materialistic ways of thinking increase alienation and that money cannot contribute to human happiness and well‐being. In addition, active participation in social activities can decrease alienation. The research results suggest that a materialistic, money‐is‐all attitude negatively influences alienation across cultures; in addition, in the US, an affluent consumption‐based country, the money‐is‐all attitude had more explanatory power for alienation than in Sweden and Korea. A change in values to overcome the money‐is‐all attitude is required and the concepts of sufficiency and mindfulness are suggested as alternative life perspectives for the pursuit of well‐being.     

RETHINKING DYNAMIC CAPITAL STRUCTURE MODELS WITH ROLL‐OVER DEBT

Dynamic capital structure models with roll‐over debt rely on widely accepted arguments that have never been formalized. This paper clarifies the literature and provides a rigorous formulation of the equity holders’ decision problem within a game theory framework. We spell out the linkage between default policies in a rational expectations equilibrium and optimal stopping theory. We prove that there exists a unique equilibrium in constant barrier strategies, which coincides with that derived in the literature. Furthermore, that equilibrium is the unique equilibrium when the firm loses all its value at default time. Whether the result holds when there is a recovery at default remains a conjecture.     

TIME‐CONSISTENT AND MARKET‐CONSISTENT EVALUATIONS

We consider evaluation methods for payoffs with an inherent financial risk as encountered for instance for portfolios held by pension funds and insurance companies. Pricing such payoffs in a way consistent to market prices typically involves combining actuarial techniques with methods from mathematical finance. We propose to extend standard actuarial principles by a new market‐consistent evaluation procedure which we call “two‐step market evaluation.” This procedure preserves the structure of standard evaluation techniques and has many other appealing properties. We give a complete axiomatic characterization for two‐step market evaluations. We show further that in a dynamic setting with continuous stock prices every evaluation which is time‐consistent and market‐consistent is a two‐step market evaluation. We also give characterization results and examples in terms of g‐expectations in a Brownian‐Poisson setting.     

Robust consumption‐investment problem under CRRA and CARA utilities with time‐varying confidence sets

We consider a robust consumption‐investment problem under constant relative risk aversion and constant absolute risk aversion utilities. The time‐varying confidence sets are specified by Θ, a correspondence from [0, T] to the space of the Lévy triplets, and describe a priori drift, volatility, and jump information. For each possible measure, the log‐price processes of stocks are semimartingales, and the triplet of their differential characteristics is almost surely a measurable selector from the correspondence Θ. By proposing and investigating the global kernel, an optimal policy and a worst‐case measure are generated from a saddle point of the global kernel, and they constitute a saddle point of the objective function.     

A FIRST‐ORDER BSPDE FOR SWING OPTION PRICING: CLASSICAL SOLUTIONS

In a companion paper, we studied a control problem related to swing option pricing in a general non‐Markovian setting. The main result there shows that the value process of this control problem can uniquely be characterized in terms of a first‐order backward stochastic partial differential equation (BSPDE) and a pathwise differential inclusion. In this paper, we additionally assume that the cash flow process of the swing option is left‐continuous in expectation. Under this assumption, we show that the value process is continuously differentiable in the space variable that represents the volume in which the holder of the option can still exercise until maturity. This gives rise to an existence and uniqueness result for the corresponding BSPDE in a classical sense. We also explicitly represent the space derivative of the value process in terms of a nonstandard optimal stopping problem over a subset of predictable stopping times. This representation can be applied to derive a dual minimization problem in terms of martingales.     

A FIRST‐ORDER BSPDE FOR SWING OPTION PRICING

We study an optimal control problem related to swing option pricing in a general non‐Markovian setting in continuous time. As a main result we uniquely characterize the value process in terms of a first‐order nonlinear backward stochastic partial differential equation and a differential inclusion. Based on this result we also determine the set of optimal controls and derive a dual minimization problem.     

Risk Minimization with Incomplete Information in a Model for High‐Frequency Data

We study risk‐minimizing hedging‐strategies for derivatives in a model where the asset price follows a marked point process with stochastic jump‐intensity, which depends on some unobservable state‐variable process. This model reflects stylized facts that are typical for high frequency data. We assume that agents in our model are restricted to observing past asset prices. This poses some problems for the computation of risk‐minimizing hedging strategies as the current value of the state variable is unobservable for our agents. We overcome this difficulty by a two‐step procedure, which is based on a projection result of Schweizer and show that in our context the computation of risk‐minimizing strategies leads to a filtering problem that has received some attention in the nonlinear filtering literature.     

MEAN‐VARIANCE POLICY FOR DISCRETE‐TIME CONE‐CONSTRAINED MARKETS: TIME CONSISTENCY IN EFFICIENCY AND THE MINIMUM‐VARIANCE SIGNED SUPERMARTINGALE MEASURE

The discrete‐time mean‐variance portfolio selection formulation, which is a representative of general dynamic mean‐risk portfolio selection problems, typically does not satisfy time consistency in efficiency (TCIE), i.e., a truncated precommitted efficient policy may become inefficient for the corresponding truncated problem. In this paper, we analytically investigate the effect of portfolio constraints on the TCIE of convex cone‐constrained markets. More specifically, we derive semi‐analytical expressions for the precommitted efficient mean‐variance policy and the minimum‐variance signed supermartingale measure (VSSM) and examine their relationship. Our analysis shows that the precommitted discrete‐time efficient mean‐variance policy satisfies TCIE if and only if the conditional expectation of the density of the VSSM (with respect to the original probability measure) is nonnegative, or once the conditional expectation becomes negative, it remains at the same negative value until the terminal time. Our finding indicates that the TCIE property depends only on the basic market setting, including portfolio constraints. This motivates us to establish a general procedure for constructing TCIE dynamic portfolio selection problems by introducing suitable portfolio constraints.