Neural network approximation for superhedging prices

This article examines neural network-based approximations for the superhedging price process of a contingent claim in a discrete time market model. First we prove that the α-quantile hedging price converges to the superhedging price at time 0 for α tending to 1, and show that the α-quantile hedging price can be approximated by a neural network-based price. This provides a neural network-based approximation for the superhedging price at time 0 and also the superhedging strategy up to maturity. To obtain the superhedging price process for $t>0$, by using the Doob decomposition, it is sufficient to determine the process of consumption. We show that it can be approximated by the essential supremum over a set of neural networks. Finally, we present numerical results.     

Distribution‐constrained optimal stopping

We solve the problem of optimal stopping of a Brownian motion subject to the constraint that the stopping time's distribution is a given measure consisting of finitely many atoms. In particular, we show that this problem can be converted to a finite sequence of state‐constrained optimal control problems with additional states corresponding to the conditional probability of stopping at each possible terminal time. The proof of this correspondence relies on a new variation of the dynamic programming principle for state‐constrained problems, which avoids measurable selections. We emphasize that distribution constraints lead to novel and interesting mathematical problems on their own, but also demonstrate an application in mathematical finance to model‐free superhedging with an outlook on volatility.     

SUPERHEDGING IN ILLIQUID MARKETS

We study superhedging of securities that give random payments possibly at multiple dates. Such securities are common in practice where, due to illiquidity, wealth cannot be transferred quite freely in time. We generalize some classical characterizations of superhedging to markets where trading costs may depend nonlinearly on traded amounts and portfolios may be subject to constraints. In addition to classical frictionless markets and markets with transaction costs or bid‐ask spreads, our model covers markets with nonlinear illiquidity effects for large instantaneous trades. The characterizations are given in terms of stochastic term structures which generalize term structures of interest rates beyond fixed income markets as well as martingale densities beyond stochastic markets with a cash account. The characterizations are valid under a topological condition and a minimal consistency condition, both of which are implied by the no arbitrage condition in the case of classical perfectly liquid market models. We give alternative sufficient conditions that apply to market models with general convex cost functions and portfolio constraints.     

Model-free portfolio theory: A rough path approach

Based on a rough path foundation, we develop a model-free approach to stochastic portfolio theory (SPT). Our approach allows to handle significantly more general portfolios compared to previous model-free approaches based on Föllmer integration. Without the assumption of any underlying probabilistic model, we prove a pathwise formula for the relative wealth process, which reduces in the special case of functionally generated portfolios to a pathwise version of the so-called master formula of classical SPT. We show that the appropriately scaled asymptotic growth rate of a far reaching generalization of Cover's universal portfolio based on controlled paths coincides with that of the best retrospectively chosen portfolio within this class. We provide several novel results concerning rough integration, and highlight the advantages of the rough path approach by showing that (nonfunctionally generated) log-optimal portfolios in an ergodic Itô diffusion setting have the same asymptotic growth rate as Cover's universal portfolio and the best retrospectively chosen one.     

ROBUST BOUNDS FOR FORWARD START OPTIONS

We consider the problem of finding a model‐free upper bound on the price of a forward start straddle with payoff . The bound depends on the prices of vanilla call and put options with maturities T₁ and T₂ , but does not rely on any modeling assumptions concerning the dynamics of the underlying. The bound can be enforced by a super‐replicating strategy involving puts, calls, and a forward transaction. We find an upper bound, and a model which is consistent with T₁ and T₂ vanilla option prices for which the model‐based price of the straddle is equal to the upper bound. This proves that the bound is best possible. For lognormal marginals we show that the upper bound is at most 30% higher than the Black–Scholes price. The problem can be recast as finding the solution to a Skorokhod embedding problem with nontrivial initial law so as to maximize .     

Would You Like to be a Prosumer? Information Revelation,Personalization and Price Discrimination in Electronic Markets

Electronic commerce and flexible manufacturing allow personalization of initially standardized products at low cost. Will customers provide the information necessary for personalization? Assuming that a consumer can control the amount of information revealed, we analyze how her decision interacts with the pricing strategy of a monopolist who may abuse the information to obtain a larger share of total surplus. We consider two scenarios, one where consumers have different tastes but identical willingness to pay and another with high and low valuation customers. In both cases full revelation may only result if the monopolist can commit to a maximum price before consumers decide about disclosure.     

NO‐ARBITRAGE PRICING FOR DIVIDEND‐PAYING SECURITIES IN DISCRETE‐TIME MARKETS WITH TRANSACTION COSTS

We prove a version of First Fundamental Theorem of Asset Pricing under transaction costs for discrete‐time markets with dividend‐paying securities. Specifically, we show that the no‐arbitrage condition under the efficient friction assumption is equivalent to the existence of a risk‐neutral measure. We derive dual representations for the superhedging ask and subhedging bid price processes of a contingent claim contract. Our results are illustrated with a vanilla credit default swap contract.     

Trust and Stakeholder Theory: Trustworthiness in the Organisation–Stakeholder Relationship

Trust is a fundamental aspect of the moral treatment of stakeholders within the organization–stakeholder relationship. Stakeholders trust the organization to return benefit or protections from harm commensurate with their contributions or stakes. However, in many situations, the firm holds greater power than the stakeholder and therefore cannot necessarily be trusted to return the aforementioned duty to the stakeholder. Stakeholders must therefore rely on the trustworthiness of the organization to fulfill obligations in accordance to Phillips’ principle of fairness (Business Ethics Quarterly 7(1), 1997, 51–66), particularly where low-power stakeholders may not be fully consenting (Van Buren III, Business Ethics Quarterly 11(3), 2001, 481–499). The construct of organizational trustworthiness developed herewith is presented as a possible solution to the problem of unfairness in organization–stakeholder relations. While organizational trustworthiness does not create an ethical obligation where none existed before, stakeholders who lack power will likely be treated fairly when organizational trustworthiness is present.     

Reverse stress testing: Scenario design for macroprudential stress tests

We propose a systematic algorithmic reverse-stress testing methodology to create “worst case” scenarios for regulatory stress tests by accounting for losses that arise from distressed portfolio liquidations. First, we derive the optimal bank response for any given shock. Then, we introduce an algorithm which systematically generates scenarios that exploit the key vulnerabilities in banks' portfolio holdings and thus maximize contagion despite banks' optimal response to the shock. We apply our methodology to data of the 2016 European Banking Authority (EBA) stress test, and design worst case scenarios for the portfolio holdings of European banks at the time. Using spectral clustering techniques, we group 10,000 worst-case scenarios into twelve geographically concentrated families. Our results show that even though there is a wide range of different scenarios within these 12 families, each cluster tends to affect the same banks. An “Anna Karenina” principle of stress testing emerges: Not all stressful scenarios are alike, but every stressful scenario stresses the same banks. These findings suggest that the precise specification of a scenario is not of primal importance as long as the most vulnerable banks are targeted and sufficiently stressed. Finally, our methodology can be used to uncover the weakest links in the financial system and thereby focus supervisory attention on these, thus building a bridge between macroprudential and microprudential stress tests.     

现行企业会计核算制度应单独考虑到物流成本

随着物流管理的迅速发展,物流成本越来越受到人们的重视。然而,物流成本都包括哪些内容,应如何管理以使其得到相对量上的降低,在理论上还不是十分清晰,在实践中也没有探索出一套切实可行的方法。如能将物流成本融入会计核算制度,以借贷记账法进行系统全面的管理,将不失为一条很好的思路。     

Why do entrepreneurs use franchising as a financial tool? An agency explanation

When and why one type of entrepreneur (franchisor) attracts to its ventures another type of entrepreneur (franchisees) instead of passive investors is a central concern in entrepreneurship literature. Based on the informativeness principle of the principal–agent model, we claim that franchisees are not such an expensive financial tool as has been argued in the literature because their compensation (return) is more efficiently designed: it directly depends on variables which are under franchisees' control. We therefore link agency and financial explanations for franchising. Most of our findings show that, once the agency argument is controlled for, the higher the cost of alternative funds for the franchisor (estimated through different variables), the more the franchisor will rely on expansion through franchising as opposed to company-ownership. We interpret this as a clue that franchising is also used as a financial capital source.     

A Microeconomic Approach to Diffusion Models For Stock Prices

This paper studies a class of diffusion models for stock prices derived by a microeconomic approach. We consider discrete-time processes resulting from a market equilibrium and then apply an invariance principle to obtain a continuous-time model. the resulting process is an Ornstein-Uhlenbeck process in a random environment, and we analyze its qualitative behavior. In particular, we provide simple criteria for the stability or instability of the corresponding stock price model, and we give explicit formulae for the invariant distributions in the recurrent case.     

Optimal Portfolios with Bounded Capital at Risk

We consider some continuous-time Markowitz type portfolio problems that consist of maximizing expected terminal wealth under the constraint of an upper bound for the capital at risk. In a Black–Scholes setting we obtain closed-form explicit solutions and compare their form and implications to those of the classical continuous-time mean-variance problem. We also consider more general price processes that allow for larger fluctuations in the returns.     

PRICING OF AMERICAN PATH-DEPENDENT CONTINGENT CLAIMS

We consider the problem of pricing path-dependent contingent claims. Classically, this problem can be cast into the Black-Scholes valuation framework through inclusion of the path-dependent variables into the state space. This leads to solving a degenerate advection-diffusion partial differential equation (PDE). We first estabilish necessary and sufficient conditions under which degenerate diffusions can be reduced to lower-dimensional nondegenerate diffusions. We apply these results to path-dependent options. Then, we describe a new numerical technique, called forward shooting grid (FSG) method, that efficiently copes with degenerate diffusion PDEs. Finally, we show that the FSG method is unconditionally stable and convergent. the FSG method is the first capable of dealing with the early exercise condition of American options. Several numerical examples are presented and discussed. ²     

Models and optimal designs for conjoint choice experiments including a no-choice option

In a classical conjoint choice experiment, respondents choose one profile from each choice set that has to be evaluated. However, in real life, the respondent does not always make a choice: often he/she does not prefer any of the options offered. Therefore, including a no-choice option in a choice set makes a conjoint choice experiment more realistic. In the literature, three different models are used to analyze the results of a conjoint choice experiment with a no-choice option: the no-choice multinomial logit model, the extended no-choice multinomial logit model, and the nested no-choice multinomial logit model. We develop optimal designs for the two most appealing of these models using the D-optimality criterion and the modified Fedorov algorithm and compare these optimal designs with a reference design, which is constructed while ignoring the no-choice option, in terms of estimation and prediction accuracy. We conclude that taking into account the no-choice option when designing a no-choice experiment only has a marginal effect on the estimation and prediction accuracy as long as the model used for estimation matches the data-generating model.     

Uncertainty,Specialization and Government Intervention

We use a one‐factor two‐sector model of comparative advantage with uncertainty to compare the effects of different specialization levels on growth under various scenarios. We derive the static and dynamic optimal level of specialization under the centralized and the decentralized economy. We identify the conditions under which the socially optimal specialization level entails positive investment in the comparatively disadvantaged sector. We show that in this case the socially optimal solution cannot be reached by the decentralized economy which is in fact characterized by over‐specialization. We conclude presenting a simple tax‐based redistributive mechanism able to achieve the optimal level of specialization in a decentralized economic system.     

Strategic Role of Retailer Bundling in a Distribution Channel

We study retailer bundling in a distribution channel when the manufacturer for one bundled product can strategically set the wholesale price. We show that the retailer can use a bundling option as a strategic leverage to extract concessions from the manufacturer in form of a lower wholesale price. This finding contributes a novel rationale for retailer bundling to the bundling literature. Whenever the bundling option causes this concession-extraction effect, the retailer always benefits from the lower wholesale price. The manufacturer, nevertheless, does not necessarily suffer because bundling can lead to a higher consumer demand. We also show that the manufacturer's marginal production cost plays a critical role in driving the retailer's bundling decision, concession extraction behavior and consequently the total channel profit.     

General equilibrium pricing of nonredundant forward contracts

We derive the general equilibrium of a dynamic financial market in which the investors' opportunity set includes nonredundant forward contracts. We show that Breeden's (1979) consumption‐based CAPM equation for forward contracts contains an extra term relative to that for cash assets. We name this term a strategy risk premium. It compensates investors for the (systematic) risk that stems from their very portfolio strategies when the latter involve nonredundant forward contracts. We also show that Merton's (1973) multibeta intertemporal CAPM must be amended for forward contracts to exhibit adjusted risk premia for the market portfolio and all relevant state variables, as opposed to the usual risk premia for cash assets. Our results are shown not to depend on the usual cash‐and‐carry relationship, which, in general, does not hold. We, nevertheless, provide a well‐known special case where it does hold, albeit not grounded on the usual no‐arbitrage argument. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:817–840, 2003     

Partitioning uncertain workloads

We present a method for determining the ratio of the tasks when breaking any complex workload in such a way that once the outputs from all tasks are joined, their full completion takes less time and exhibit smaller variance than when running on the undivided workload. To do that, we have to infer the capabilities of the processing unit executing the divided workloads or tasks. We propose a Bayesian Inference algorithm to infer the amount of time each task takes in a way that does not require prior knowledge on the processing unit capability. We demonstrate the effectiveness of this method in two different scenarios; the optimization of a convex function and the transmission of a large computer file over the Internet. Then we show that the Bayesian inference algorithm correctly estimates the amount of time each task takes when executed in one of the processing units.