Now, Later, or Both: A Closed-Form Optimal Decision for a Risk-Averse Buyer

Motivated by the energy domain, we examine a risk-averse buyer that has to purchase a fixed quantity of a continuous good. The buyer has two opportunities to buy: now or later. The buyer can spread the quantity over the two timeslots in any way, as long as the total quantity remains the same. The current price is known, but the future price is not. It is well known that risk neutral buyers purchase in whichever timeslot they expect to be the cheapest, regardless of the uncertainty of the future price. Research suggests, however, that most people may in fact be risk-averse. If the expected future price is lower than the current price, but very uncertain, then they may purchase in the present, or spread the quantity over both timeslots. We describe a formal model with a uniform price distribution and a two-segment piecewise linear risk aversion function. We provide a theorem that states the optimal decision as a closed-form expression.

[1]  A. Tversky,et al.  Prospect theory: analysis of decision under risk , 1979 .

[2]  A. Tversky,et al.  Prospect Theory : An Analysis of Decision under Risk Author ( s ) : , 2007 .

[3]  Sven Koenig,et al.  Risk-averse auction agents , 2003, AAMAS '03.

[4]  Valentin Robu,et al.  Designing bidding strategies in sequential auctions for risk averse agents , 2010, Multiagent Grid Syst..

[5]  Valdinei Freire da Silva,et al.  Shortest Stochastic Path with Risk Sensitive Evaluation , 2012, MICAI.

[6]  L. Tesfatsion,et al.  An Agent-Based Test Bed Study of Wholesale Power Market Performance Measures , 2008, IEEE Computational Intelligence Magazine.

[7]  Sven Koenig,et al.  Probabilistic Planning with Nonlinear Utility Functions , 2006, ICAPS.

[8]  Bart Selman,et al.  Risk-Sensitive Policies for Sustainable Renewable Resource Allocation , 2011, IJCAI.

[9]  Han La Poutré,et al.  Reduction of Market Power and Stabilisation of Outcomes in a Novel and Simplified Two-Settlement Electricity Market , 2012, 2012 IEEE/WIC/ACM International Conferences on Web Intelligence and Intelligent Agent Technology.

[10]  Maria L. Gini,et al.  Harnessing the search for rational bid schedules with stochastic search and domain-specific heuristics , 2004, Proceedings of the Third International Joint Conference on Autonomous Agents and Multiagent Systems, 2004. AAMAS 2004..

[11]  Nicholas R. Jennings,et al.  A Risk-Based Bidding Strategy for Continuous Double Auctions , 2004, ECAI.

[12]  Mathijs de Weerdt,et al.  The 2014 Power Trading Agent Competition , 2014 .

[13]  R. Thaler,et al.  Anomalies: Risk Aversion , 2001 .

[14]  Nicholas R. Jennings,et al.  Bidding strategies for realistic multi-unit sealed-bid auctions , 2008, Autonomous Agents and Multi-Agent Systems.

[15]  Mathijs de Weerdt,et al.  The 2017 Power Trading Agent Competition , 2013 .

[16]  P. Wakker.  Explaining the characteristics of the power (CRRA) utility family. , 2008, Health economics.

[17]  M. J. Sobel,et al.  Discounted MDP's: distribution functions and exponential utility maximization , 1987 .

[18]  Vedran Podobnik,et al.  An Analysis of Power Trading Agent Competition 2014 , 2014, AMEC/TADA.

[19]  Jurica Babic,et al.  Adaptive Bidding for Electricity Wholesale Markets in a Smart Grid , 2014 .

[20]  K. Arrow,et al.  Aspects of the theory of risk-bearing , 1966 .

[21]  Jaroslava Hlouskova,et al.  Optimal asset allocation under linear loss aversion , 2011 .

[22]  Daniel Urieli,et al.  TacTex'13: A Champion Adaptive Power Trading Agent , 2014, AAAI.

[23]  Ping Hou,et al.  Revisiting Risk-Sensitive MDPs: New Algorithms and Results , 2014, ICAPS.

[24]  Wolfgang Ketter,et al.  Autonomous Agents in Future Energy Markets: The 2012 Power Trading Agent Competition , 2013, AAAI.

[25]  M. Best,et al.  Loss-Aversion with Kinked Linear Utility Functions , 2014 .

[26]  Han La Poutré,et al.  A Successful Broker Agent for Power TAC , 2014, AMEC/TADA.

[27]  Kenneth J. Arrow,et al.  Aspects of the Theory of Risk Bearing--Yrjo Jahnsson Lectures , 1969 .