Associate Professor Traian A Pirvu
Mathematics & Statistics - McMaster University
My main research lies in the area of financial mathematics with a special emphasis on optimal investment and pricing in incomplete markets. My projects are on equilibrium pricing of non tradable risks, optimal portfolio selection with regulatory constraints, time consistent portfolio management, prospect theory, insurance mathematics, and mathematical economics.
Editorial Activities
Editorial Board Member
• Advisory Board Member for Computer Sciences & Mathematics Forum
• Topical Advisor Panel for Risks
Guest Editor
• Guest Editor in Risks on a Special Issue on Systemic Risk
• Guest Editor in Risks on a Special Issue on Mathematical Methods Applied in Pricing and Investment Problems
Journal Referee for over 30 journals: Econometrica, Annals of Applied Probability, Journal of Banking and Finance, SIAM Journal of Controland Optimization, Finance and Stochastics, Mathematical Finance, Journal of Economics Dynamics and Control, Mathematics of Operations Research, SIAM Journal on Financial Mathematics, Annals of Operations Research, Math Control Related Fields, Insurance: Mathematics and Economics, Quantitative Finance, Journal of Optimization Theory and Applications, Mathematical and Financial Economics, Proceedings of AMS, Mathematical Social Sciences, Journal of Mathematical Economics, ESAIM: Control, Optimization and Calculus of Variations, ASTIN Bulletin: The Journal of the IAA The Journal of the International Actuarial Association, Scandinavian Actuarial Journal, Computational and Applied Mathematics, Studies in Nonlinear, Dynamics and Econometrics, Communications in Statistics, The Journal of Risk, International Journal of Theoretical and Applied Finance, Computational Management Science, Annals of Finance, Journal of Economics, Finance Research Letters, and others.
Publications
Published/Accepted for Publication
• T. A. Pirvu, On the discontinuities of real valued functions (2003), in Romanian, Sfera
• K. Larsen, T. A. Pirvu, S. E. Shreve, R. Tutuncu, Satisfying Convex Risk Limits by Trading, Finance & Stochastics (2005), 9, 177-195
• T. A. Pirvu, Portfolio Optimization under the Value-at-Risk Constraint, Quantitative Finance (2007), 7, 125-136
• I. Ekeland, and T. A. Pirvu, Investment and Consumption without Commitment, Mathematics and Financial Economics (2008), 2, 57-86
• T. A. Pirvu, and G. Zitkovic, Maximizing Portfolio Growth Rate under Risk Constraints, Mathematical Finance (2009), 19 (3), 423-455
• T. A. Pirvu, and U. G. Haussmann, Time Consistent Utility Maximization, Canadian Applied Mathematics Quarterly (2009), 17, 721-737
• U. Horst, T. A. Pirvu, and G. D. Reis, On Securitization, Market Completion and Equilibrium Risk Transfer, Mathematics and Financial Economics (2010), 2, 211-252
• I. Ekeland, O. Mbodji and T. A. Pirvu, Time Consistent Portfolio Management, SIAM Journal on Financial Mathematics (2012), 3, 57-86
• T. A. Pirvu and K. Schulze, Multi-Stock Portfolio Optimization under Prospect Theory, Mathematics and Financial Economics (2012), 6(4), 337-362
• T. A. Pirvu and H. Zhang, Optimal Investment, Consumption and Life Insurance under Mean-Reverting Returns: The Complete Market Solution, Insurance: Mathematics and Economics (2012), 51(2), 303-309
• T. A. Pirvu and H. Zhang, Utility Indifference Pricing: A Time Consistent Approach, Applied Mathematical Finance (2013), 20(4), 304-326
• S. Moreno-Bromberg, T. A. Pirvu and A. Reveilac, CRRA Utility Maximization under Risk Constraints, Communication on Stochastic Analysis (2013), 7(2), 203-225
• S. Jewell, Y. Li and T. A. Pirvu, Non-Linear Equity Portfolio Variance Reduction under Delta-Gamma Approach Analysis, Operations Research Letters (2013), 41(6), 694-700
• M. Kwak, T. A. Pirvu and H. Zhang, A Multi Period Equilibrium Pricing Model, Journal of Applied Mathematics (2014), Volume 2014, 1-14
• A. Shidfara, K. Paryaba, A. R. Yazdanian and T. A. Pirvu, Numerical analysis for Spread option pricing model of markets with finite liquidity: First-order feedback model, International Journal of Computer Mathematics (2014), Volume 2014, 1-18
• E. C. Canepa and T. A. Pirvu, An application of the double Skorokhod formula, Interdisciplinary Topics in Applied Mathematics, Modelling, and Computational Science, Springer Procedings in Mathematics & Statistics (2014), Vol.117
• T. A. Pirvu and H. Zhang, Investment-Consumption with regime-switching discount rate, Mathematics Social Sciences (2014), 71, 142-150
• P. S. N. Gambrah and T. A. Pirvu, Risk Measures and Portfolio Optimization, Journal of Risk and Financial Management (2015), 7, 113-129
• P. Cheridito, U. Horst, M. Kupper, and T. A. Pirvu, Equilibrium in Incomplete Markets under Translation Invariant Preferences, Mathematics of Operation Research (2016), 41 (1), 174-195
• A. R. Yazdanian and T. A. Pirvu, Numerical analysis for Spread option pricing model of markets with finite liquidity: Full feedback model, Applied Mathematics & Information Sciences (2016), 10 (4), 1271-1281
• F. Pourbabaee, M. Kwak and T. A. Pirvu, Risk minimization and portfolio diversification, Quantitative Finance (2016), 9, 1325-1332
• M. Metel, T. A. Pirvu, and J. Wong, Risk Management under Omega Measure, Risks (2017), 5(2), 1-14
• M. Kwak and T. A. Pirvu, Cumulative Prospect Theory with Skewed Return Distribution, SIAM Journal on Financial Mathematics (2018), 9(1), 54-89.
• T.A. Pirvu and U.G. Haussmann, An Extension of Clark-Haussman Formula and Applications, Stochastics An International Journal of Probability and Stochastic Processes (Stochastics), (2019), 91(6), 895-904.
• C. E. Canepa and T. A. Pirvu, A mathematical model and the optimal strategy in the transactions between one bank and the central bank, Proceedings of the Romanian Academy-series A: Mathematics, Physics, Technical Sciences, Information Science (2019), 20(2), 107-115.
• L. Deng and T. A. Pirvu, Multi-period investment strategies under Cumulative Prospect Theory, Journal of Risk and Financial Management, (2019), 12(2), 83, 1-15.
• O. Mbodji, A. Nguyen Huu, and T. A. Pirvu, Optimal consumption for a couple of agents sharing a portfolio, Mathematics Social Sciences, (2019), 101, 88-98.
• D. P. Covei, and T. A. Pirvu, An elliptic partial differential equation and its application, Applied Mathematics Letters, (2020), 101, 1-8.
• A. Maheshwari and T. A. Pirvu, Portfolio Optimization under Correlation Constraint, Risks, (2020), 8(1), 15, 1-19.
• E. C. Canepa, D. P. Covei, and T. A. Pirvu, A Stochastic production planning problem, Fixed Point Theory, Volume 23 (1) (2022), 179-198.
• D. P. Covei, and T. A. Pirvu, A Stochastic Control Problem with Regime Switching, Carpathian Journal of Mathematics, (2021), Volume 37 (3), 427-440.
• P. Jevtic, M. Kwak and T. A. Pirvu, Practical Partial Equilibrium Framework for Pricing of Mortality-Linked Instruments in Continuous Time, European Actuarial Journal, (2022), 12 (1), 249-273.
• E. C. Canepa, and T. A. Pirvu, A Funds Market Bank Problem, U.P.B. Sci. Bull., Series A, Vol. 84, (2022) Iss. 3, 103-110.
•. E. C. Canepa, D. P. Covei, and T. A. Pirvu, On a Stochastic production planning with regime switching, (2023) J. Ind. Manag. Optim, Volume 19, Issue 3, 2023, 1697-1713.
• P. Jevtic, T. A. Pirvu, S. Cahyaningtias, and T. Tran, Minimizing bankruptcy probability of a life insurer - some analytical considerations, U.P.B. Sci. Bull, (2023), 85(4), 91-100.
• D. P. Covei, T. A. Pirvu, and C. Sterbeti, A Population model with pseudo exponential survival, Carpathian Journal of Mathematics, (2024), Volume 40(3), 629-643.
• D. P. Covei, T. A. Pirvu, and C. Sterbeti, The Equilibrium Solutions for a Nonlinear Separable Population Model, Mathematics, (2024), 12(273) (2024), 1-15.
• S. Zhang, and T. A. Pirvu, Spread Option Pricing under Finite Liquidity Framework, (2024), Risks, 12(11), 173.
Submitted for Publication
• K. Z. Zhang, and T. A. Pirvu, Numerical Simulation of Exchange Option with Finite Liquidity: Controlled Variate Model
https://arxiv.org/abs/2006.07771
• K. Z. Zhang, and T. A. Pirvu, Pricing spread option with liquidity adjustments
https://arxiv.org/abs/2101.00223
• O. Mbodji, and T. A. Pirvu, Time consistency and utility weighted discount rates
https://arxiv.org/abs/2402.05113
• X. Gao, C. Hyndman, P. Jevtic and T. A. Pirvu, Optimal annuitization post-retirement with labor income
https://arxiv.org/abs/2202.04220
Books
Book Chapters
• T. A. Pirvu Chapter 2 in Quantitative Fund Management, edited by M. Dempster, G. Pflug, and G. Mitra, Taylor & Francis, (2008) Boca Raton.