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We formulate quantum computing solutions to a large class of dynamic nonlinear asset pricing models using algorithms, in theory exponentially more efficient than classical ones, which leverage the quantum properties of superposition and entanglement. The equilibrium asset pricing solution is a quantum state. We introduce quantum decision-theoretic foundations of ambiguity and model/parameter uncertainty to deal with model selection., Comment: 51 pages, 4 figures

We present a classical enhancement to improve the accuracy of the Hybrid variant (Hybrid HHL) of the quantum algorithm for solving liner systems of equations proposed by Harrow, Hassidim, and Lloyd (HHL). We achieve this by using higher precision quantum estimates of the eigenvalues relevant to the linear system, and an enhanced classical processing step to guide the eigenvalue inversion part of Hybrid HHL. We show that eigenvalue estimates with just two extra bits of precision results in tighter error bounds for our Enhanced Hybrid HHL compared to HHL. We also show that our enhancement reduces the error of Hybrid HHL by an average of 57 percent on an ideal quantum processor for a representative sample of 2x2 systems. On IBM Hanoi and IonQ Aria-1 hardware, we see that the error of Enhanced Hybrid HHL algorithm is on average 13 percent and 20 percent (respecitvely) less than that of HHL for a similar set of 2x2 systems. Finally, we use simulated eigenvalue estimates to perform an inversion of a 4x4 matrix on IonQ Aria-1 with a fidelity of 0.61. To our knowledge this is the largest HHL implementation with a fidelity greater than 0.5., Comment: 9 pages, 4 figures, submitted to QCE24

Quantum computers are not yet up to the task of providing computational advantages for practical stochastic diffusion models commonly used by financial analysts. In this paper we introduce a class of stochastic processes that are both realistic in terms of mimicking financial market risks as well as more amenable to potential quantum computational advantages. The type of models we study are based on a regime switching volatility model driven by a Markov chain with observable states. The basic model features a Geometric Brownian Motion with drift and volatility parameters determined by the finite states of a Markov chain. We study algorithms to estimate credit risk and option pricing on a gate-based quantum computer. These models bring us closer to realistic market settings, and therefore quantum computing closer the realm of practical applications.