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Register a new userSequential Detection of Market shocks using Risk-averse Agent Based Models
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Vikram Krishnamurthy
Publication date
2015
fields
Financial
and research's language is
English
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This paper considers a statistical signal processing problem involving agent based models of financial markets which at a micro-level are driven by socially aware and risk- averse trading agents. These agents trade (buy or sell) stocks by exploiting information about the decisions of previous agents (social learning) via an order book in addition to a private (noisy) signal they receive on the value of the stock. We are interested in the following: (1) Modelling the dynamics of these risk averse agents, (2) Sequential detection of a market shock based on the behaviour of these agents. Structural results which characterize social learning under a risk measure, CVaR (Conditional Value-at-risk), are presented and formulation of the Bayesian change point detection problem is provided. The structural results exhibit two interesting prop- erties: (i) Risk averse agents herd more often than risk neutral agents (ii) The stopping set in the sequential detection problem is non-convex. The framework is validated on data from the Yahoo! Tech Buzz game dataset.
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Multistage risk-averse optimal control problems with nested conditional risk mappings are gaining popularity in various application domains. Risk-averse formulations interpolate between the classical expectation-based stochastic and minimax optimal control. This way, risk-averse problems aim at hedging against extreme low-probability events without being overly conservative. At the same time, risk-based constraints may be employed either as surrogates for chance (probabilistic) constraints or as a robustification of expectation-based constraints. Such multistage problems, however, have been identified as particularly hard to solve. We propose a decomposition method for such nested problems that allows us to solve them via efficient numerical optimization methods. Alongside, we propose a new form of risk constraints which accounts for the propagation of uncertainty in time.
The multi-armed bandit (MAB) is a classical online optimization model for the trade-off between exploration and exploitation. The traditional MAB is concerned with finding the arm that minimizes the mean cost. However, minimizing the mean does not take the risk of the problem into account. We now want to accommodate risk-averse decision makers. In this work, we introduce a coherent risk measure as the criterion to form a risk-averse MAB. In particular, we derive an index-based online sampling framework for the risk-averse MAB. We develop this framework in detail for three specific risk measures, i.e. the conditional value-at-risk, the mean-deviation and the shortfall risk measures. Under each risk measure, the convergence rate for the upper bound on the pseudo regret, defined as the difference between the expectation of the empirical risk based on the observation sequence and the true risk of the optimal arm, is established.
Consider a multi-agent network comprised of risk averse social sensors and a controller that jointly seek to estimate an unknown state of nature, given noisy measurements. The network of social sensors perform Bayesian social learning - each sensor fuses the information revealed by previous social sensors along with its private valuation using Bayes rule - to optimize a local cost function. The controller sequentially modifies the cost function of the sensors by discriminatory pricing (control inputs) to realize long term global objectives. We formulate the stochastic control problem faced by the controller as a Partially Observed Markov Decision Process (POMDP) and derive structural results for the optimal control policy as a function of the risk-aversion factor in the Conditional Value-at-Risk (CVaR) cost function of the sensors. We show that the optimal price sequence when the sensors are risk- averse is a super-martingale; i.e, it decreases on average over time.
We describe three independent implementations of a new agent-based model (ABM) that simulates a contemporary sports-betting exchange, such as those offered commercially by companies including Betfair, Smarkets, and Betdaq. The motivation for constructing this ABM, which is known as the Bristol Betting Exchange (BBE), is so that it can serve as a synthetic data generator, producing large volumes of data that can be used to develop and test new betting strategies via advanced data analytics and machine learning techniques. Betting exchanges act as online platforms on which bettors can find willing counterparties to a bet, and they do this in a way that is directly comparable to the manner in which electronic financial exchanges, such as major stock markets, act as platforms that allow traders to find willing counterparties to buy from or sell to: the platform aggregates and anonymises orders from multiple participants, showing a summary of the market that is updated in real-time. In the first instance, BBE is aimed primarily at producing synthetic data for in-play betting (also known as in-race or in-game betting) where bettors can place bets on the outcome of a track-race event, such as a horse race, after the race has started and for as long as the race is underway, with betting only ceasing when the race ends. The rationale for, and design of, BBE has been described in detail in a previous paper that we summarise here, before discussing our comparative results which contrast a single-threaded implementation in Python, a multi-threaded implementation in Python, and an implementation where Python header-code calls simulations of the track-racing events written in OpenCL that execute on a 640-core GPU -- this runs approximately 1000 times faster than the single-threaded Python. Our source-code for BBE is freely available on GitHub.
This paper introduces an intermediary between conditional expectation and conditional sublinear expectation, called R-conditioning. The R-conditioning of a random-vector in $L^2$ is defined as the best $L^2$-estimate, given a $sigma$-subalgebra and a degree of model uncertainty. When the random vector represents the payoff of derivative security in a complete financial market, its R-conditioning with respect to the risk-neutral measure is interpreted as its risk-averse value. The optimization problem defining the optimization R-conditioning is shown to be well-posed. We show that the R-conditioning operators can be used to approximate a large class of sublinear expectations to arbitrary precision. We then introduce a novel numerical algorithm for computing the R-conditioning. This algorithm is shown to be strongly convergent. Implementations are used to compare the risk-averse value of a Vanilla option to its traditional risk-neutral value, within the Black-Scholes-Merton framework. Concrete connections to robust finance, sensitivity analysis, and high-dimensional estimation are all treated in this paper.
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