Short note on inf-convolution preserving the Fatou property

We model agents’ preferences by cash-invariant concave functionals defined on L ^∞, and formulate the optimal risk allocation problem as their infimal-convolution. We study the case of agents whose choice functionals are law-invariant with respect to different probability measures and show how, in this case, the value function preserves a desirable dual representation (equivalent to the Fatou property). Financial support from the European Science Foundation (ESF) “Advanced Mathematical Methods for Finance” (AMaMeF) under the exchange grant 1192 is gratefully acknowledged.     

The efficient hedging problem for American options

In this paper, we prove the existence of efficient partial hedging strategies for a trader unable to commit the initial minimal amount of money needed to implement a hedging strategy for an American option. The attitude towards the shortfall is modeled in terms of a decreasing and convex risk functional satisfying a lower semicontinuity property with respect to the Fatou convergence of stochastic processes. Some relevant examples of risk functionals are analyzed. Numerical computations in a discrete-time market model are provided. In a Lévy market, an approximating solution is given assuming discrete-time trading.     

Comparative and qualitative robustness for law-invariant risk measures

When estimating the risk of a P&L from historical data or Monte Carlo simulation, the robustness of the estimate is important. We argue here that Hampel’s classical notion of qualitative robustness is not suitable for risk measurement, and we propose and analyze a refined notion of robustness that applies to tail-dependent law-invariant convex risk measures on Orlicz spaces. This concept captures the tradeoff between robustness and sensitivity and can be quantified by an index of qualitative robustness. By means of this index, we can compare various risk measures, such as distortion risk measures, in regard to their degree of robustness. Our analysis also yields results of independent interest such as continuity properties and consistency of estimators for risk measures, or a Skorohod representation theorem for ψ-weak convergence.     

Consistent Variance Curve Models

We introduce a general approach to model a joint market of stock price and a term structure of variance swaps in an HJM-type framework. In such a model, strongly volatility-dependent contracts can be priced and risk-managed in terms of the observed stock and variance swap prices. To this end, we introduce equity forward variance term structure models and derive the respective HJM-type arbitrage conditions. We then discuss finite-dimensional Markovian representations of the fixed time-to-maturity forward variance swap curve and derive consistency results for both the standard case and for variance curves with values in a Hilbert space. For the latter, our representation also ensures non-negativity of the process. We then give a few examples of such variance curve functionals and briefly discuss completeness and hedging in such models. As a further application, we show that the speed of mean reversion in some standard stochastic volatility models should be kept constant when the model is recalibrated.     

Optimal investment-consumption-insurance with random parameters

This paper discusses an optimal investment, consumption, and life insurance purchase problem for a wage earner in a complete market with Brownian information. Specifically, we assume that the parameters governing the market model and the wage earner, including the interest rate, appreciation rate, volatility, force of mortality, premium-insurance ratio, income and discount rate, are all random processes adapted to the Brownian motion filtration. Our modeling framework is very general, which allows these random parameters to be unbounded, non-Markovian functionals of the underlying Brownian motion. Suppose that the wage earner’s preference is described by a power utility. The wage earner’s problem is then to choose an optimal investment-consumption-insurance strategy so as to maximize the expected, discounted utilities from intertemporal consumption, legacy and terminal wealth over an uncertain lifetime horizon. We use a novel approach, which combines the Hamilton–Jacobi–Bellman equation and backward stochastic differential equation (BSDE) to solve this problem. In general, we give explicit expressions for the optimal investment-consumption-insurance strategy and the value function in terms of the solutions to two BSDEs. To illustrate our results, we provide closed-form solutions to the problem with stochastic income, stochastic mortality, and stochastic appreciation rate, respectively.     

Fast estimation of true bounds on Bermudan option prices under jump-diffusion processes

Fast pricing of American-style options has been a difficult problem since it was first introduced to the financial markets in 1970s, especially when the underlying stocks’ prices follow some jump-diffusion processes. In this paper, we extend the ‘true martingale algorithm’ proposed by Belomestny et al. [Math. Finance, 2009, 19, 53–71] for the pure-diffusion models to the jump-diffusion models, to fast compute true tight upper bounds on the Bermudan option price in a non-nested simulation manner. By exploiting the martingale representation theorem on the optimal dual martingale driven by jump-diffusion processes, we are able to explore the unique structure of the optimal dual martingale and construct an approximation that preserves the martingale property. The resulting upper bound estimator avoids the nested Monte Carlo simulation suffered by the original primal–dual algorithm, therefore significantly improving the computational efficiency. Theoretical analysis is provided to guarantee the quality of the martingale approximation. Numerical experiments are conducted to verify the efficiency of our algorithm.     

On Haezendonck risk measures

We study the Haezendonck risk measure (introduced by [Haezendonck, J., Goovaerts, M., 1982. A new premium calculation principle based on Orlicz norms. Insurance: Mathematics and Economics 1, 41–53] and by [Goovaerts, M.J., Kaas, R., Dhaene, J., Tang, Q., 2003. A unified approach to generate risk measures. ASTIN Bulletin 33 (2), 173–191; Goovaerts, M.J., Kaas, R., Dhaene, J., Tang, Q., 2004. Some new classes of consistent risk measures. Insurance: Mathematics and Economics 34 (3), 505–516]) and prove its subadditivity. Since the Haezendonck risk measure is defined as an infimum of Orlicz premia, we investigate when the infimum is actually attained. We determine the corresponding generalized scenarios and show how its construction can be seen as a special case of the operation of inf-convolution of convex functionals.     

Depreciation-Related Capital Gains,Differential Tax Rates,and the Market Value of Real Estate Investment Trusts

We develop a model for valuing U.S. real estate investment trusts (REITs) that considers the tax liability impounded in REITs’ property portfolios. This liability is a function of the portfolio’s accumulated depreciation and is driven by different tax rates applied to individual components of the total gain from property sales. These two components are the capital gain resulting from the sale of property at a price higher than its cost and the gain due to the recapture of depreciation taken during the use of the property. Our measure of value is the REIT’s net asset liquidation value (NALV). The metric of REIT value currently used by analysts is a REIT’s net asset value (NAV), but a REIT’s NAV will always be greater than the NALV and therefore overestimate market value, all else equal. Finally, using observed market prices for REITs, we provide evidence that NALVs give superior estimates of REIT market prices than do NAVs.     

Superreplication under model uncertainty in discrete time

We study the superreplication of contingent claims under model uncertainty in discrete time. We show that optimal superreplicating strategies exist in a general measure-theoretic setting; moreover, we characterize the minimal superreplication price as the supremum over all continuous linear pricing functionals on a suitable Banach space. The main ingredient is a closedness result for the set of claims which can be superreplicated from zero capital; its proof relies on medial limits.     

A generalized probability framework to model economic agents' decisions under uncertainty

The applications of techniques from statistical (and classical) mechanics to model interesting problems in economics and finance have produced valuable results. The principal movement which has steered this research direction is known under the name of ‘econophysics’. In this paper, we illustrate and advance some of the findings that have been obtained by applying the mathematical formalism of quantum mechanics to model human decision making under ‘uncertainty’ in behavioral economics and finance. Starting from Ellsberg's seminal article, decision making situations have been experimentally verified where the application of Kolmogorovian probability in the formulation of expected utility is problematic. Those probability measures which by necessity must situate themselves in Hilbert space (such as ‘quantum probability’) enable a faithful representation of experimental data. We thus provide an explanation for the effectiveness of the mathematical framework of quantum mechanics in the modeling of human decision making. We want to be explicit though that we are not claiming that decision making has microscopic quantum mechanical features.     

Dynamic programming approach to principal–agent problems

We consider a general formulation of the principal–agent problem with a lump-sum payment on a finite horizon, providing a systematic method for solving such problems. Our approach is the following. We first find the contract that is optimal among those for which the agent’s value process allows a dynamic programming representation, in which case the agent’s optimal effort is straightforward to find. We then show that the optimization over this restricted family of contracts represents no loss of generality. As a consequence, we have reduced a non-zero-sum stochastic differential game to a stochastic control problem which may be addressed by standard tools of control theory. Our proofs rely on the backward stochastic differential equations approach to non-Markovian stochastic control, and more specifically on the recent extensions to the second order case.     

Risk management in local authorities: An application of Schatzki's social site ontology

Prior research has devoted limited attention to studying changes in organisational risk management (RM) practices. This is despite continuous dissatisfaction from academics and practitioners with organisations' ability to manage risks. We draw on Schatzki's social site ontology to study RM practices of two New Zealand local authorities that both experienced (earthquake) risk events and whose RM practices could be expected to change. We extend recent research utilising Schatzki, by finding that practical intelligibility and general understanding mutually affect each other in the organising of practices. Further, we extend Nama and Lowe’s (2014) addition to Schatzki by highlighting the importance of including teleological structures and accounting devices into the mutually constitutive relationship between general understanding and affectivity. Finally, we contribute to RM literature by proposing that changing the general understanding (in addition to the mere implementation of RM tools) is an important way of making RM change fundamental and sustainable.     

Beyond cash-additive risk measures: when changing the numéraire fails

We discuss risk measures representing the minimum amount of capital a financial institution needs to raise and invest in a pre-specified eligible asset to ensure it is adequately capitalized. Most of the literature has focused on cash-additive risk measures, for which the eligible asset is a risk-free bond, on the grounds that the general case can be reduced to the cash-additive case by a change of numéraire. However, discounting does not work in all financially relevant situations, especially when the eligible asset is a defaultable bond. In this paper, we fill this gap by allowing general eligible assets. We provide a variety of finiteness and continuity results for the corresponding risk measures and apply them to risk measures based on value-at-risk and tail value-at-risk on L ^p spaces, as well as to shortfall risk measures on Orlicz spaces. We pay special attention to the property of cash subadditivity, which has been recently proposed as an alternative to cash additivity to deal with defaultable bonds. For important examples, we provide characterizations of cash subadditivity and show that when the eligible asset is a defaultable bond, cash subadditivity is the exception rather than the rule. Finally, we consider the situation where the eligible asset is not liquidly traded and the pricing rule is no longer linear. We establish when the resulting risk measures are quasiconvex and show that cash subadditivity is only compatible with continuous pricing rules.     

Commercial Property Rent Dynamics in U.S. Metropolitan Areas: An Examination of Office, Industrial, Flex and Retail Space

This paper is concerned with the market rental rate for space offered by commercial property and how that rental rate evolves over time. Rental rates reflect the value of the services provided by the property and can have a significant impact on the ability of its owners to make monthly debt obligations. We investigate commercial property rent dynamics for 34 large metropolitan areas in the U.S. The dynamics are studied from the second quarter of 1990 through the second quarter of 2009 and the results are compared across four property types or uses (office, industrial, flex, and retail). There is substantial heterogeneity in both the long and short run responses to changing demand and supply conditions. In general, the office market is the slowest to adjust back towards equilibrium while industrial and flex markets adjust back to the long run equilibrium very quickly. For industrial and office types, the speed of adjustment is substantially faster within quality segments and is strongest for grade A properties.     

Risk Management as Passionate Imitation: The Interconnections Among Emotions,Performance Metrics,and Risk in a Global Technology Firm

This paper traces the evolution of risk management practices in a global technology company between 2000 and 2015. We extend recent research that has highlighted the emotional aspects of riskwork. We detail how a passionate interest—‘we can do better at risk management’—emotionally ‘hooked’ the staff in the company's Sourcing Unit. Risk management, emotion, and management controls were intertwined. When top management singled out one of the key metrics clearly as a risk‐related metric for the Sourcing Unit, the employees felt a strong sense of relief, which gave rise to subsequent extensive risk measurement. We also contribute to the more general debate about accounting and its entanglement with emotions. Little is known about the ‘birth’ and the reasons for durability of passionate interests. Following Tarde (1903/2013), such ‘birth’ and endurance can be explained by analyzing how passionate imitation emerges as a result of a series of dislocal events—in our case a fire, new performance metrics, and natural disasters. These events triggered emotions that provided the necessary energy for three forms of passionate imitation: a) ‘we need to imitate our main competitor’ and risk mapping; b) ‘others in the organization are imitating us and our suppliers should imitate us’ and risk measurement; and c) ‘others in the organization (more specifically the Product Development Unit) should imitate us’ and proactive risk avoidance. This passionate imitation helped explain why the sourcing staff continued to be emotionally ‘hooked’ to risk management, that is, how the passionate interest endured and became vested.     

中国城际高铁与商业信用供给——基于准自然实验的研究

本文利用中国城际高铁开通对公司产品质量保证动机产生的外生变化来考察其如何影响公司的商业信用供给决策。高铁开通通过降低运输成本,提高了公司与客户之间的交易量,不仅可以降低公司与客户之间的信息不对称,还可以促使公司提高产品质量,削弱了公司为了保证产品质量而提供商业信用的动机。借助高铁开通在时间和空间上错列发生的特征,构建准自然实验情境,本文使用双重差分方法的检验,结果表明高铁开通使公司商业信用供给减少约3.51%。研究发现,交易量提高是高铁开通减少公司商业信用供给的重要渠道。进一步分析发现,对于事前信息不对称程度较大、关系专用性投资水平较高和产品质量保证需求较低的公司,高铁开通导致公司商业信用供给减少更多。本文研究为商业信用供给的产品质量保证理论提供了进一步的补充和发展,研究结论对于理解交通基础设施的经济效应以及公司商业信用供给决策的影响因素具有一定的启示意义。     

Taking the ontological and materialist turns: Agential realism,representation theory,and accounting information systems

Karen Barad’s (2007) agential realism conceives the world as intra-acting agencies that take definite form only when an agential cut is made. In the information systems discipline, her theory underpins much of the work that goes under the rubric of sociomateriality. Importantly, her work challenges the validity of theories about the world based on representationalism and so-called Cartesian dualism. At least some scholars who subscribe to sociomateriality argue that one consequence of Barad’s theory is that information systems theories such as representation theory stand on shaky grounds. I subject this proposition to scrutiny. I begin by summarizing the major tenets of representation theory and agential realism. Next, I use agential realism to provide an account of phenomena that are associated with an accounting information systems case study. I then evaluate the account, particularly from the perspective of what novel, innovative insights occur by using an agential realism lens. Compared to existing theories such as actor-network theory and general systems theory, I conclude that little new is learned. Moreover, I argue that representation theory provides an alternative, robust account of the case-study phenomena. I also consider the question of whether agential realism potentially provides accounting information systems scholars with a means of identifying the core of their field and constructing theories about any core they might identify.     

A fuzzy-based approach to residual income equity valuation

The decision of whether to buy, hold or sell equities depends on whether the current price reflects the stock’s intrinsic or fundamental value. The residual income valuation model expresses this fundamental value as a function of current book value of equity plus the sum of discounted expected residual income. Although past and present income and book value information is readily available to investors, values taken by essential parameters in this model are unknown ex ante, particularly the cost of equity or discount rate and future residual income. Any point estimate of equities’ fundamental value according to the model may therefore conceal considerable variation around the estimate, even in the presence of minor perturbations in the model’s inputs. In this paper, we introduce a fuzzy-based approach which reflects the imprecision inherent in certain parameters in equity valuation. We extend the limited prior fuzzy-based literature on investment analysis by introducing the concept of fuzzy fundamental equity value, initially on an illustrative example. To further demonstrate this fuzzy representation, illustrative financial statement data for individual UK companies are considered, with fuzzy fundamental equity values evaluated over progressive forecast horizons. Our series of illustrative applications (which encompasses the standard crisp approach) make the inherent uncertainty involved in estimating equity value immediately apparent.     

Prediction of Individual Bond Prices via a Dynamic Bond Pricing Model: Application to Japanese Government Bond Price Data

In this paper, we propose a dynamic bond pricing model and report the usefulness of our bond pricing model based on analysis of Japanese Government bond price data. We extend the concept of the time dependent Markov (TDM) model proposed by Kariya and Tsuda (Financial Engineering and the Japanese Markets, Kluwer Academic Publishers, Dordrecht, The Netherlands, Vol. 1, pp. 1–20) to a dynamic model, which can obtain information for future bond prices. A main feature of the extended model is that the whole stochastic process of the random cash-flow discount functions of each individual bond has a time series structure. We express the dynamic structure for the models by using a Bayesian state space representation. The state space approach integrates cross-sectional and time series aspects of individual bond prices. From the empirical results, we find useful evidence that our model performs well for the prediction of the patterns of the term structure of the individual bond returns.