Final Payoff Research Articles

Gender Differences in Intra-Household Efficiency: Evidence from an Investment Game Between Spouses in India

In this paper, I test for gender differences in intra-household allocative efficiency through a laboratory experiment with established married couples in India. The experiment presents the couple with the opportunity to earn 50 per cent of daily household expenditure. Spouses played an investment game where one spouse was randomly assigned to the role of sender and the other to receiver. The setting of the game is unique in several ways. There is perfect information over strategies, actions, and final payoffs. Second mover spouses can react to the first movers’ actions, which is rare in intra-household experiments. The unitary and cooperative models of the household are rejected as only 5 per cent of men and 2 per cent of women in the sender role play the household earnings maximising strategy. Women send significantly less money than their male counterparts. Women (senders) who keep more money are those in households where husbands’ tobacco consumption is largest costing households the equivalent of 30 per cent of daily household expenditure. The results indicate that households operate under non-cooperative bargaining contracts where women are willing to incur costs to maintain control over money.

Analyzing the interest rate risk of equity-indexed annuities via scenario matrices

The financial return of equity-indexed annuities depends on an underlying fund or investment portfolio complemented by an investment guarantee. We discuss a so-called cliquet-style or ratchet-type guarantee granting a minimum annual return. Its path-dependent payoff complicates valuation and risk management, especially if interest rates are modelled stochastically. We develop a novel scenario-matrix (SM) method. In the example of a Vasicek-Black-Scholes model, we derive closed-form expressions for the value and moment-generating function of the final payoff in terms of the scenario matrix. This allows efficient evaluation of values and various risk measures, avoiding Monte-Carlo simulation or numerical Fourier inversion. In numerical tests, this procedure proves to converge quickly and outperforms the existing approaches in the literature in terms of computation time and accuracy.

On the bailout dividend problem with periodic dividend payments for spectrally negative Markov additive processes

This paper studies the bailout optimal dividend problem with regime switching under the constraint that dividend payments can be made only at the arrival times of an independent Poisson process while capital can be injected continuously in time. We show the optimality of the regime-modulated Parisian-classical reflection strategy when the underlying risk model follows a general spectrally negative Markov additive process. In order to verify the optimality, first we study an auxiliary problem driven by a single spectrally negative Lévy process with a final payoff at an exponential terminal time and characterize the optimal dividend strategy. Then, we use the dynamic programming principle to transform the global regime-switching problem into an equivalent local optimization problem with a final payoff up to the first regime switching time. The optimality of the regime modulated Parisian-classical barrier strategy can be proven by using the results from the auxiliary problem and approximations via recursive iterations.

Estimation of Initial Stock in Pollution Control Problem

A two-player differential game of pollution control with uncertain initial disturbance stock is considered. In pace with contemporary policy in the resource extraction industry, we initiate our research based on a resource extraction differential model with a rehabilitation process in which the firms are required to compensate the local to rehabilitate the polluted and dilapidated areas. Given the reality that the initial pollution stock plays a critical role in the production, and we cannot rigorously determine its actual value, a simulation of the estimation of the initial stock is alternatively investigated through the Pontryagin maximum principle (PMP). The later analytical results by normalized value of information (NVI) indicate the precious influence brought to the final payoff under various estimations of the initial stock both in the cooperative and non-cooperative cases. With such guidance, the player is capable of making a much more judicious decision when it comes to the determination of the initial stock. Furthermore, a numerical example is additionally presented for better comprehension.

Long-term relationships, group lending, and peer monitoring in microfinance: Experimental evidence

Microfinance is generally associated with high repayment rates. However, it is not clear what drives such high repayment rates? Does the success of microfinance results only from the use of group lending, peer sanctioning or long-term relationships that typically characterize microfinance contracts? In this paper, we aim to contribute to the existing literature by using a laboratory experiment to disentangle the effect of these different potential mechanisms. Our experiment involves both students and real bankers in the role of lenders. We find that group lending alone, in absence of peer sanctioning mechanisms induces free riding and is not sufficient to mitigate the problems of ex ante and ex post moral hazard. In sharp contrast, we find that individualized long-term relationships perform significantly better than either form of group lending with or without peer sanctioning. Consequently, borrowers’ final payoffs are lower in the group lending schemes than in the individual lending scheme due to the fact that borrowers receive on average fewer loans from lenders in the group lending schemes. Our study also sheds light on the social cost of peer pressure mechanisms.

Community energy projects in the context of generation and transmission expansion planning

We extend multi-level generation and transmission expansion planning optimisation methods to analyse the impact of the community energy sector emergence on power system expansion. Methodologically, we do this by incorporating biform games and linear production games into the classic power transmission and generation expansion planning problem. The model is formulated as a Mathematical Program with Equilibrium Constraints (MPEC). Using a stylised example based on Chilean power market data, we show that community energy projects can be an optimal choice for residential customers. Furthermore, we find that community energy projects can widely impact the power system as a whole. Importantly, unlike some large generation projects, they can have positive effects on electricity customers who do not participate in them. Nevertheless, the implementation of net billing schemes, potential competitors for community energy projects, may be preferred when net billing injection prices are comparatively high, there are potentially high levels of confidence about the final payoffs, and there exist comparatively lower investment costs. Yet, we show that, depending on the specific case analysed with our model, it is likely that under the above circumstances nodal prices increase, social welfare decreases, and capacity limitations need to be addressed. The methodology developed in this work can be a valuable tool to examine and better understand the complexities of community energy projects and their interactions with market incumbents.

Pricing barrier options with deep backward stochastic differential equation methods

This paper presents a novel and direct approach to solving boundary- and final-value problems, corresponding to barrier options, using forward pathwise deep learning and forward–backward stochastic differential equations (FBSDEs). Barrier instruments are instruments that expire or transform into another instrument if a barrier condition is satisfied before maturity; otherwise they perform like the instrument without the barrier condition. In a partial differential equation, this corresponds to adding boundary conditions to the final-value problem. The deep backward stochastic differential equation (deep BSDE) methods developed so far have not addressed barrier/boundary conditions directly. We extend the pathwise deep BSDE methods to the barrier condition case by adding nodes to the computational graph, in order to explicitly monitor the barrier conditions for each realization of the dynamics, as well as adding nodes that preserve the time, state variables and trading strategy value at the barrier breach, or at maturity otherwise. Given these additional nodes in the computational graph, the forward loss function quantifies the replication of the barrier or final payoff according to a chosen risk measure such as the squared sum of differences. The proposed method can handle any barrier condition in the FBSDE setup and any Dirichlet boundary conditions in the partial differential equation setup, in both low and high dimensions.

Self-reported & revealed trust: Experimental evidence

I study the relationship between self-declared trust attitudes – using a well-recognised and established personality questionnaire — and trust choices in an induced infinitely repeated trust game. I find that self-reported trust measures are significantly related with trust choices as long as trust is part of equilibrium strategies. I find that questions regarding others’ intentions is a missing component in previous work that studies self-reports of trust. An important aspect of the design is that first movers are not privy to the choices made by their partners. This design feature, coupled with an uncertainty element introduced in determining the first mover’s final payoff, allows me to analyse how first movers react to bad outcomes. Trusting individuals are more likely to give the benefit of doubt to others. Analysis of the incentivised subjective beliefs reveals that the effect of personality traits on trust choices is not through the formation of beliefs.

Intelligence, Errors, and Cooperation in Repeated Interactions

Abstract We study how strategic interaction and cooperation are affected by the heterogeneity of cognitive skills of groups of players, over consecutive plays of repeated games with randomly matched opponents using Prisoner’s Dilemma as stage game. We observe overall higher cooperation rates and average final payoffs in integrated treatment groups—where subjects of different IQ levels interact together—than in separated treatment groups. Lower IQ subjects are better off and higher IQ subjects are worse off in integrated groups than in separated groups. Higher IQ subjects adopt harsher strategies when they are pooled with lower IQ subjects than when they play separately. We demonstrate that this outcome should be expected in learning and evolutionary models where higher intelligence subjects exhibit lower frequency of errors in the implementation of strategies. Estimations of errors and strategies in our experimental data are consistent with the model’s assumptions and predictions.

COSLE: Cost sensitive loan evaluation for P2P lending

The loan evaluation is a fundamental task in peer-to-peer (P2P) lending. Effective loan evaluation can help lenders make informed investment decisions. Existing methods do not consider the return of loans in the core learning stage and thus fail to explore the relationship between the return of loans and their final loan payoff outcomes. In this study, we propose a systematic loan evaluation framework called COst Sensitive Loan Evaluation (COSLE). Specifically, we first develop an instance-aware misclassification cost (IMCO) matrix, which specifies personalized cost for each loan. Then, we present a differential labelling algorithm called DILA cost for assigning node labels and assessing the corresponding cost. By integrating these enhancements into the tree-induction process, we construct a node splitting measurement called COG index. It exploits the relationship between the return information and the final payoff outcome. Additionally, we design the LER evaluation metric to measure the ability of a loan evaluation model to increase the lender’s return. Finally, the COSLE is used to improve popular tree models. Extensive experiments based on the Lending Club dataset show that our COSLE can effectively increase the lender’s return.

The effects of reputation on inequality in network cooperation games.

In the last several decades, ample evidence from across evolutionary biology, behavioural economics and econophysics has solidified our knowledge that reputation can promote cooperation across different contexts and environments. Higher levels of cooperation entail higher final payoffs on average, but how are these payoffs distributed among individuals? This study investigates how public and objective reputational information affects payoff inequality in repeated social dilemma interactions in large groups. I consider two aspects of inequality: excessive dispersion of final payoffs and diminished correspondence between final payoff and cooperative behaviour. I use a simple heuristics-based agent model to demonstrate that reputational information does not always increase the dispersion of final payoffs in strategically updated networks, and actually decreases it in randomly rewired networks. More importantly, reputational information almost always improves the correspondence between final payoffs and cooperative behaviour. I analyse empirical data from nine experiments of the repeated Trust, Helping, Prisoner's Dilemma and Public Good games in networks of ten or more individuals to provide partial support for the predictions. Our research suggests that reputational information not only improves cooperation but may also reduce inequality.This article is part of the theme issue ‘The language of cooperation: reputation and honest signalling'.

Effectiveness of Artificial Neural Networks in Hedging against WTI Crude Oil Price Risk

Despite the growing share of renewable energy sources, most of the world energy supply is still based on hydrocarbons and the vast majority of world transport is fuelled by oil products. Thus, the profitability of many companies may depend on the effective management of oil price risk. In this article, we analysed the effectiveness of artificial neural networks in hedging against the risk of WTI crude oil prices increase. This was reformulated from a regressive problem to a classification problem. The effectiveness of our approach, using artificial neural networks to classify observations, was verified for over ten years of WTI futures quotes, starting from 2009. The data analysis presented in this paper confirmed that the buyer of a call option was more often likely to incur a loss as a result of its purchase than make a profit after the final payoff from the call option. The results of the conducted research confirm that neural networks can be an effective form of protection against the risk of price fluctuations. The effectiveness of a network’s operation depends on the choice of assessment indicators, but analyses show that the networks which, for the indicator that was selected, gave the best results for the training set, also resulted in positive rates of return for the test set. Significantly, we also showed interdependence between seemingly unrelated indicators: percentage of the best possible results achieved in the analysed period of time by the proposed method and percentage of all available call options that were purchased based on the results from the networks that were used.

Equity-linked Guaranteed Minimum Death Benefits with dollar cost averaging

In this paper, we analyze a form of equity-linked Guaranteed Minimum Death Benefit (GMDB), whose payoff depends on a dollar cost averaging (DCA) style periodic investment in the risky index, with rider premiums paid at regular intervals. This rider is a very natural insurance vehicle for equity-linked variable annuities, and the DCA feature has a tendency to reduce the uncertainty associated with the final payoff, beyond the minimum benefit guaranteed to the beneficiary upon death of the insured. This makes the insurer risk easier to manage as the contract ages. From the policyholder's perspective, the protection is cheaper than a standard GMDB whose payoff depends solely on the risky index value upon death, but still offers the upside potential from an investment made at regular intervals. We derive closed-form valuation formulas under the fairly broad class of exponential Lévy models for the risky index, which includes Black-Scholes as a special case. Closed-form valuation is provided by a fundamental link between this contract and a series of Asian options, for which valuation is well established. We provide several valuation strategies, and demonstrate the soundness of the framework.

Cautious farsighted stability in network formation games with streams of payoffs

We propose a new notion of farsighted pairwise stability for dynamic network formation which includes two notable features: consideration of intermediate payoffs and cautiousness. This differs from existing concepts which typically consider either only immediate or final payoffs, and which often require that players are optimistic in any environment without full communication and commitment. For arbitrary (and possibly heterogeneous) preferences over the process of network formation, a non-empty cautious path stable set of networks always exists. Furthermore, some general relationships exist between cautious path stability and other farsighted concepts.

The equal-surplus Shapley value for chance-constrained games on finite sample spaces

Many interactions from linear production problems, financial markets, or sequencing problems are modeled by cooperative games where payoffs to a coalition of players is a random variable. For this class of cooperative games, we introduce a two-stage value as an ex-ante agreement among players. Players are first promised their prior Shapley shares which are exactly their respective shares by the Shapley value of the expectation game. The final payoff vector is obtained by equally re-allocating the surplus when a realization of the random payoff of the grand coalition is observed. In support of the tractability of the newly introduced value called equal-surplus Shapley value, we provide a simple and compact formula. Depending on which probability distributions over the sample spaces are admissible, we present several characterization results of the equal-surplus Shapley value. This is achieved by using some classical axioms together with some other appealing axioms such as the independence of local duplication which simply requires that individual shares in a game remain unchanged when only certain events are duplicated in the sample space of a coalition without altering the probability of observing the others.

Assessing reinforcement delta hedging

Usual option pricing is based on replication assuming complete markets. Complete markets means that simple hedging strategies, like delta hedging, work exactly but real markets are not complete. This has motivated research on reinforcement learning to develop pricing for incomplete markets that are highly complex to deal with otherwise. However, the literature has studied approximations of reinforcement learning giving the agents hints, e.g. approximated payoffs before the actual final payoff, or by using a neural network for each timestep, increasing complexity. Here, we investigate if a single agent can learn hedging without hints, i.e. by only knowing the final pay-off, using reinforcement learning. We consider the simplest possible option setup: a vanilla European equity option in a pure Black-Scholes world. We use an agent-critic-based method, Deep Deterministic Policy Gradient (DDPG), and show that even in this simplest case, DDPG alone is unable to properly hedge. However, by employing ensemble methods, i.e. average and median, we can significantly improve accuracy and stability. This emphasises the need for customization in the application of deep learning in hedging rather than being purely driven by data and hyper-parameters.

Pricing Barrier Options with DeepBSDEs

This paper presents a novel and direct approach to price boundary and final-value problems, corresponding to barrier options, using forward deep learning to solve forward-backward stochastic differential equations (FBSDEs). Barrier instruments are instruments that expire or transform into another instrument if a barrier condition is satisfied before maturity; otherwise they perform like the instrument without the barrier condition. In the PDE formulation, this corresponds to adding boundary conditions to the final value problem. The deep BSDE methods developed so far have not addressed barrier/boundary conditions directly. We extend the forward deep BSDE to the barrier condition case by adding nodes to the computational graph to explicitly monitor the barrier conditions for each realization of the dynamics as well as nodes that preserve the time, state variables, and trading strategy value at barrier breach or at maturity otherwise. Given these additional nodes in the computational graph, the forward loss function quantifies the replication of the barrier or final payoff according to a chosen risk measure such as squared sum of differences. The proposed method can handle any barrier condition in the FBSDE set-up and any Dirichlet boundary conditions in the PDE set-up, both in low and high dimensions.

Cybersecurity Capacity: Does It Matter?

Abstract National cybersecurity capacity building involves the development of managerial, technical, social, legal, policy, and regulatory initiatives by a growing ecology of actors to enhance the resilience of nations to cybersecurity breaches, cybercrime, and terrorism. Capacity building is therefore resource intensive, requiring attention across sectors of society, ranging from governments to Internet users. However, it is difficult to justify commitments to capacity building when the benefits of building national cybersecurity capacity are largely based on logical reasoning, limited case studies, anecdotal evidence, and expert opinion rather than systematic empirical evidence. To explore the value of capacity building, this article reports on the early phase of a systematic effort to bring together cross-national data from multiple sources to examine whether indicators related to the cybersecurity capacity of a nation help explain the experiences of Internet users—one of the final payoffs of cybersecurity capacity building.

Cybersecurity Capacity: Does It Matter?

Abstract National cybersecurity capacity building involves the development of managerial, technical, social, legal, policy, and regulatory initiatives by a growing ecology of actors to enhance the resilience of nations to cybersecurity breaches, cybercrime, and terrorism. Capacity building is therefore resource intensive, requiring attention across sectors of society, ranging from governments to Internet users. However, it is difficult to justify commitments to capacity building when the benefits of building national cybersecurity capacity are largely based on logical reasoning, limited case studies, anecdotal evidence, and expert opinion rather than systematic empirical evidence. To explore the value of capacity building, this article reports on the early phase of a systematic effort to bring together cross-national data from multiple sources to examine whether indicators related to the cybersecurity capacity of a nation help explain the experiences of Internet users—one of the final payoffs of cybersecurity capacity building.

Uncertainty in cooperative interval games: how Hurwicz criterion compatibility leads to egalitarianism

We study cooperative interval games. These are cooperative games where the value of a coalition is given by a closed real interval specifying a lower bound and an upper bound of the possible outcome. For interval cooperative games, several (interval) solution concepts have been introduced in the literature. We assume that each player has a different attitude towards uncertainty by means of the so-called Hurwicz coefficients. These coefficients specify the degree of optimism that each player has so that an interval becomes a specific payoff. We show that a classical cooperative game arises when applying the Hurwicz criterion to each interval game. On the other hand, the same Hurwicz criterion can also be applied to any interval solution of the interval cooperative game. Given this, we say that a solution concept is Hurwicz compatible if the two procedures provide the same final payoff allocation. When such compatibility is possible, we characterize the class of compatible solutions, which reduces to the egalitarian solution when symmetry is required. The Shapley value and the core solution cases are also discussed.