Chain or Channel? Payment Optimization with Heterogeneous Flow

45 Pages Posted: 23 Jan 2025

See all articles by Nazem Khan

Nazem Khan

University of Oxford

Paolo Guasoni

Boston University - Department of Mathematics and Statistics; Dublin City University - School of Mathematical Sciences; University of Bologna - Department of Statistics

Date Written: December 06, 2024

Abstract

Payment-channel networks (PCNs) such as the Lightning Network enable offchain payments secured by the channels' balances as alternatives to on-chain transactions. This paper solves the optimal channel management problem for two agents who pay each other arbitrarily distributed amounts. Agents optimally choose the channel's size and whether to make each payment on-chain or on-channel, depending on their current balance. With unidirectional flows, payments below some balancedependent chain amount happen on-channel while others on-chain. As the balance falls below the reserve level, payments are always made on-channel if feasible. Below the refill level, the channel is reset to its initial state. Symmetric bidirectional flows entail distinct chain thresholds and reset levels for both directions, but channels may last indefinitely. Asymmetric flows lead to a more complex optimal policies, in which both, either, or no party resets the channel. The paper characterizes optimal channels and payment policies, describing an algorithm to obtain them, given payments' frequency and distribution.

Keywords: payments, lightning network, point processes, stochastic control

Suggested Citation

Khan, Nazem and Guasoni, Paolo and Guasoni, Paolo, Chain or Channel? Payment Optimization with Heterogeneous Flow (December 06, 2024). Available at SSRN: https://ssrn.com/abstract=5046421 or http://dx.doi.org/10.2139/ssrn.5046421

Nazem Khan (Contact Author)

University of Oxford ( email )

Mansfield Road
Oxford, Oxfordshire OX1 4AU
United Kingdom

Paolo Guasoni

Boston University - Department of Mathematics and Statistics ( email )

Boston, MA 02215
United States

Dublin City University - School of Mathematical Sciences ( email )

Dublin
Ireland

HOME PAGE: http://www.guasoni.com

University of Bologna - Department of Statistics ( email )

Bologna, 40126
Italy

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