64 citations · 258 across the 10 of their papers we have counts for
10 papers
High order Bellman equations and weakly chained diagonally dominant tensors
Parsiad Azimzadeh, Erhan Bayraktar
We introduce high order Bellman equations, extending classical Bellman equations to the tensor setting. We introduce weakly chained diagonally dominant (w.c.d.d.) tensors and show…
Impulse Control in Finance: Numerical Methods and Viscosity Solutions
Parsiad Azimzadeh
The goal of this thesis is to provide efficient and provably convergent numerical methods for solving partial differential equations (PDEs) coming from impulse control problems mot…
On the CNOT-complexity of CNOT-PHASE circuits
Matthew Amy, Parsiad Azimzadeh, Michele Mosca
We study the problem of CNOT-optimal quantum circuit synthesis over gate sets consisting of CNOT and Z-basis rotations of arbitrary angles. We show that the circuit-polynomial corr…
Convergence of implicit schemes for Hamilton-Jacobi-Bellman quasi-variational inequalities
Parsiad Azimzadeh, Erhan Bayraktar, George Labahn
In [Azimzadeh, P., and P. A. Forsyth. "Weakly chained matrices, policy iteration, and impulse control." SIAM J. Num. Anal. 54.3 (2016): 1341-1364], we outlined the theory and imple…
A fast and stable test to check if a weakly diagonally dominant matrix is a nonsingular M-matrix
Parsiad Azimzadeh
We present a test for determining if a substochastic matrix is convergent. By establishing a duality between weakly chained diagonally dominant (w.c.d.d.) L-matrices and convergent…
A zero-sum stochastic differential game with impulses, precommitment, and unrestricted cost functions
Parsiad Azimzadeh
We study a zero-sum stochastic differential game (SDG) in which one controller plays an impulse control while their opponent plays a stochastic control. We consider an asymmetric s…
Stock loans with liquidation
Parsiad Azimzadeh
We derive a "semi-analytic" solution for a stock loan in which the lender forces liquidation when the loan-to-collateral ratio drops beneath a certain threshold. We use this to stu…
Fast Engset computation
Parsiad Azimzadeh, Tommy Carpenter
The blocking probability of a finite-source bufferless queue is a fixed point of the Engset formula, for which we prove existence and uniqueness. Numerically, the literature sugges…
Weakly chained matrices, policy iteration, and impulse control
Parsiad Azimzadeh, Peter A. Forsyth
This work is motivated by numerical solutions to Hamilton-Jacobi-Bellman quasi-variational inequalities (HJBQVIs) associated with combined stochastic and impulse control problems.…
The existence of optimal bang-bang controls for GMxB contracts
Parsiad Azimzadeh, Peter A. Forsyth
A large collection of financial contracts offering guaranteed minimum benefits are often posed as control problems, in which at any point in the solution domain, a control is able…