# Research articles for the 2019-12-29

A Multicriteria Decision Making Approach to Study the Barriers to the Adoption of Autonomous Vehicles
Alok Raj,J Ajith Kumar,Prateek Bansal
arXiv

The automation technology is emerging, but the adoption rate of autonomous vehicles (AV) will largely depend upon how policymakers and the government address various challenges such as public acceptance and infrastructure development. This study proposes a five-step method to understand these barriers to AV adoption. First, based on a literature review followed by discussions with experts, ten barriers are identified. Second, the opinions of eighteen experts from industry and academia regarding inter-relations between these barriers are recorded. Third, a multicriteria decision making (MCDM) technique, the grey-based Decision-making Trial and Evaluation Laboratory (Grey-DEMATEL), is applied to characterize the structure of relationships between the barriers. Fourth, robustness of the results is tested using sensitivity analysis. Fifth, the key results are depicted in a causal loop diagram (CLD), a systems thinking approach, to comprehend cause-and-effect relationships between the barriers. The results indicate that the lack of customer acceptance (LCA) is the most prominent barrier, the one which should be addressed at the highest priority. The CLD suggests that LCA can be rather mitigated by addressing two other prominent, yet more tangible, barriers -- lack of industry standards and the absence of regulations and certifications. The study's overarching contribution thus lies in bringing to fore multiple barriers to AV adoption and their potential influences on each other. Moreover, the insights from this study can help associations related to AVs prioritize their endeavors to expedite AV adoption. From the methodological perspective, this is the first study in transportation literature that integrates Grey-DEMATEL with systems thinking.

A Stochastic Investment Model for South African Use
Şule Şahin,Shaun Levitan
arXiv

The need for stochastic modelling is on the rise globally in the pension, life insurance and investment industries due to both an increase in regulation and a natural requirement for stochastic analysis in modelling exercises. Research in the area of stochastic models or recently called economic scenario generators for actuarial use in South Africa has largely been limited. The seminal papers in this regard have a number of practical limitations. In this paper, we propose a stochastic investment model for South Africa by modelling price inflation rates, share dividends, long term and short-term interest rates for the period 1960-2018 and inflation-linked bonds for the period 2000-2018. Possible by-directional relations between the economic series have been considered and the model is designed to provide long-term forecasts that should find application in long-term modelling for both pension funds and life insurance companies.

Alpha Discovery Neural Network based on Prior Knowledge
Jie Fang,Zhikang Xia,Xiang Liu,Shutao Xia,Yong Jiang,Jianwu Lin
arXiv

In financial automatic feature construction task, genetic programming is the state-of-the-art-technic. It uses reverse polish expression to represent features and then uses genetic programming to simulate the evolution process. With the development of deep learning, there are more powerful feature extractors for option. And we think that comprehending the relationship between different feature extractors and data shall be the key. In this work, we put prior knowledge into alpha discovery neural network, combined with different kinds of feature extractors to do this task. We find that in the same type of network, simple network structure can produce more informative features than sophisticated network structure, and it costs less training time. However, complex network is good at providing more diversified features. In both experiment and real business environment, fully-connected network and recurrent network are good at extracting information from financial time series, but convolution network structure can not effectively extract this information.

Dynamics of the Price Behavior in Stock Market: A Statistical Physics Approach
Hung T. Diep,Gabriel Desgranges
arXiv

We study in this paper the time evolution of stock markets using a statistical physics approach. Each agent is represented by a spin having a number of discrete states $q$ or continuous states, describing the tendency of the agent for buying or selling. The market ambiance is represented by a parameter $T$ which plays the role of the temperature in physics. We show that there is a critical value of $T$, say $T_c$, where strong fluctuations between individual states lead to a disordered situation in which there is no majority: the numbers of sellers and buyers are equal, namely the market clearing. We have considered three models: $q=3$ ( sell, buy, wait), $q=5$ (5 states between absolutely buy and absolutely sell), and $q=\infty$. The specific measure, by the government or by economic organisms, is parameterized by $H$ applied on the market at the time $t_1$ and removed at the time $t_2$. We have used Monte Carlo simulations to study the time evolution of the price as functions of those parameters. Many striking results are obtained. In particular we show that the price strongly fluctuates near $T_c$ and there exists a critical value $H_c$ above which the boosting effect remains after $H$ is removed. This happens only if $H$ is applied in the critical region. Otherwise, the effect of $H$ lasts only during the time of the application of $H$. The second party of the paper deals with the price variation using a time-dependent mean-field theory. By supposing that the sellers and the buyers belong to two distinct communities with their characteristics different in both intra-group and inter-group interactions, we find the price oscillation with time.

Gauge transformations in the dual space, and pricing and estimation in the long run in affine jump-diffusion models
Svetlana Boyarchenko,Sergei Levendorskiĭ
arXiv

We suggest a simple reduction of pricing European options in affine jump-diffusion models to pricing options with modified payoffs in diffusion models. The procedure is based on the conjugation of the infinitesimal generator of the model with an operator of the form $e^{i\Phi(-i\dd_x)}$ (gauge transformation in the dual space). A general procedure for the calculation of the function $\Phi$ is given, with examples. As applications, we consider pricing in jump-diffusion models and their subordinated versions using the eigenfunction expansion technique, and estimation of the extremely rare jumps component. The beliefs of the market about yet unobserved extreme jumps and pricing kernel can be recovered: the market prices allow one to see "the shape of things to come".

Maximising with-profit pensions without guarantees
arXiv

Currently, pension providers are running into trouble mainly due to the ultra-low interest rates and the guarantees associated to some pension benefits. With the aim of reducing the pension volatility and providing adequate pension levels with no guarantees, we carry out mathematical analysis of a new pension design in the accumulation phase. The individual's premium is split into the individual and collective part and invested in funds. In times when the return from the individual fund exits a predefined corridor, a certain number of units is transferred to or from the collective account smoothing in this way the volatility of the individual fund. The target is to maximise the total accumulated capital, consisting of the individual account and a portion of the collective account due to a so-called redistribution index, at retirement by controlling the corridor width. We also discuss the necessary and sufficient conditions that have to be put on the redistribution index in order to avoid arbitrage opportunities for contributors.

Multivariate Systemic Optimal Risk Transfer Equilibrium
Alessandro Doldi,Marco Frittelli
arXiv

A Systemic Optimal Risk Transfer Equilibrium (SORTE) was introduced in "Systemic Optimal Risk Transfer Equilibrium" for the analysis of the equilibrium among financial institutions or in insurance-reinsurance markets. A SORTE conjugates the classical B\"uhlmann's notion of an equilibrium risk exchange with a capital allocation principle based on systemic expected utility optimization. In this paper we extend such notion to the case in which the value function to be optimized has two components, one being the sum of the single agents' utility functions, the other consisting of a truly systemic component. The latter could be either enforced by an external regulator or be agreed on by the participants in the market. Technically, the extension of SORTE to the new setup requires developing a theory for multivariate utility functions and selecting at the same time a suitable framework for the duality theory. Conceptually, this more general framework allows us to introduce and study a Nash Equilibrium property of the optimizer. We prove existence, uniqueness, Pareto optimality and the Nash Equilibrium property of the newly defined Multivariate Systemic Optimal Risk Transfer Equilibrium.

Robust XVA
Maxim Bichuch,Agostino Capponi,Stephan Sturm
arXiv

We introduce an arbitrage-free framework for robust valuation adjustments. An investor trades a credit default swap portfolio with a risky counterparty, and hedges credit risk by taking a position in defaultable bonds. The investor does not know the return rate of her counterparty bond, but is confident that it lies within an uncertainty interval. We derive both upper and lower bounds for the XVA process of the portfolio, and show that these bounds may be recovered as solutions of nonlinear ordinary differential equations. The presence of collateralization and closeout payoffs leads to important differences with respect to classical credit risk valuation. The value of the super-replicating portfolio cannot be directly obtained by plugging one of the extremes of the uncertainty interval in the valuation equation, but rather depends on the relation between the XVA replicating portfolio and the close-out value throughout the life of the transaction. Our comparative statics analysis indicates that credit contagion has a nonlinear effect on the replication strategies and on the XVA.

The equivalent constant-elasticity-of-variance (CEV) volatility of the stochastic-alpha-beta-rho (SABR) model
Jaehyuk Choi,Lixin Wu
arXiv

This study presents new analytic approximations of the stochastic-alpha-beta-rho (SABR) model. Unlike existing studies that focus on the equivalent Black-Scholes (BS) volatility, we instead derive the equivalent volatility under the constant-elasticity-of-variance (CEV) model, which is the limit of the SABR model when the volatility of volatility approaches 0. Numerical examples demonstrate the accuracy of the CEV volatility approximation for a wide range of parameters. Moreover, in our approach, arbitrage occurs at a lower strike price than in existing BS-based approximations.