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# No-arbitrage Pricing in a Market for Position on a Multilane Freeway (Prof. Henry Schellhorn, CGU)

## January 25, 2023 @ 4:15 pm - 5:30 pm

**Title:** No-arbitrage Pricing in a Market for Position on a Multilane Freeway

**Speaker:** Henry Schellhorn, Department of Mathematics, Claremont Graduate University

**Abstract:** We introduce a trading mechanism allowing cars to change position in a multilane congested freeway by doing peer-to-peer transactions. For the car initiating the operation, or incoming car, the goal can be to increase speed, to have less speed variability, to join a platoon, or to join an exit lane that is slower but full. We focus in this paper on the maneuver where the incoming car changes lanes by asking an adjacent car on a busy target lane (to the left or right) to slow down, but we also consider the case where the incoming car asks the car in front of it to change lanes, so that the incoming car takes its position but stays on the same lane. In both cases, the incoming car pays a transaction fee. We solve the microscopic problem of determining these transaction fees by (i) embedding the problem in a macroscopic model and (ii) calculating fair lane prices by the no arbitrage condition. This no-arbitrage condition states that no future trajectory will always be better than all others in terms of both speed and money exchanged to change lanes. The terms “always better” has to be understood in a probabilistic sense: we analyze a stochastic model, in order to include uncertainty in both the speed model and the drivers’ decisions. We highlight the advantages of no-arbitrage theory over a traditional expected utility maximization approach. First, no-arbitrage pricing does not require any individual data, whether on the driver’s risk-aversion, preference of speed over money or increased safety, or final destination. Second, the macroscopic model that we use considers endogenously the global impact of any individual priced transaction, as opposed to local models that require extraneous assumptions on the road conditions after the transaction. We implemented a simple case of our priced lane change model. After simulating it extensively, we implemented it in real-time, with 2 cars trading position on a freeway using macroscopic speed information to determine the transaction fee.

Henry Schellhorn is professor of mathematics at Claremont Graduate University’s Institute of Mathematics Sciences and academic director of the Financial Engineering Program at the Drucker School of Management. His research focuses in the areas of Monte Carlo simulation, credit risk management, interest rate models, queuing theory, and combinatorial auctions.