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Dergiler / TOJSAT / 2012 / Volume: 2 Issue: 3

Numerical Properties of Stochastic Linear Quadratic Model with Applications in Finance

Ivan Ivanov(Faculty of Economics and Business Administration St. Kliment Ohridsky, Sofia University Sofia, Bulgaria)
Boyan Lomev(Faculty of Economics and Business Administration St. Kliment Ohridsky, Sofia University Sofia, Bulgaria)
Dergi
TOJSAT
Sayfa
—
Yayın Tarihi
2016-07-23
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Finally, in order to demonstrate the efficiency of the proposed algorithms, computational examples are provided and numerical effectiveness of the considered algorithms is commented

📌 3 Maddede Bu Makale

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Amaç & Hipotez:The aim of this paper is to consider the characteristics of the numerical equilibrium solution of the stochastic linear quadratic models (SLQ) along with possible applications in financial modelling.
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Temel Bulgular & Veri:The purpose of this approach is to find feedback control function that maximizes the portfolio value keeping the condition that stock prices are modeled by stochastic differential equation.
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Sonuç & Katkı:Finally, in order to demonstrate the efficiency of the proposed algorithms, computational examples are provided and numerical effectiveness of the considered algorithms is commented
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Stochastic linear-quadratic control · Generalized algebraic Riccati equation · Positive definite solution

Abstract

The aim of this paper is to consider the characteristics of the numerical equilibrium solution of the stochastic linear quadratic models (SLQ) along with possible applications in financial modelling. The purpose of this approach is to find feedback control function that maximizes the portfolio value keeping the condition that stock prices are modeled by stochastic differential equation. Two iterations – the Newton iteration and the Lyapunov iteration for solving the generalized algebraic Riccati equation, associated with the stochastic linear-quadratic problem in an infinite time horizon are discussed. We compare these iterations with the approach based on the solution to a semidefinite programming problem. Finally, in order to demonstrate the efficiency of the proposed algorithms, computational examples are provided and numerical effectiveness of the considered algorithms is commented

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Bu Makaleye Atıf Yap

Ivanov, I., Lomev, B. (2016). Numerical Properties of Stochastic Linear Quadratic Model with Applications in Finance. TOJSAT, Volume: 2 Issue: 3. https://ajindex.com/articles/1660377

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Kaynakça (10)

  1. Damm, T., & Hinrichsen, D. (2001). Newton's method for a rational matrix equation occurring in stochastic control. Linear Algebra Appl., 332-334, 81-109.
  2. Ivanov, I. (2007). Iterations for solving a rational Riccati equation arising in stochastic control. Computers and Mathematics with Applications 53, 977-988.
  3. Ivanov, I., & Lomev, B. (2009). Iterations for stochastic models with applications in finance. Paper presented at the First International EBES Conference, Istanbul.
  4. Ivanov, I. B. Lomev, N. Netov, An Optimal Solution to Dynamic Game Models with Economic Applications, Conference Proceedings of the 7th International Conference on Applied Financial Economics, 2010: 473-479, ISSN 1792- 3912, Greece.
  5. Lin, Y. L. Bao, Y. Wei, On the generalized structure-preserving doubling algorithm for generalized discrete-time algebraic Riccati equations, Journal of Information & Computational Science 8: 6 (2011) 987–996.
  6. Rami, M., Zhou, X., & Moore, J. (2000). Well-posedness and attainability of indefinite stochastic linear quadratic control in infinite time horizon. Systems & Control Letters, 41, 123-133.
  7. Rami, M., & Zhou, X. (2000). Linear matrix inequalities, Riccati equations, and indefinite stochastic linear quadratic controls. IEEE Transactions on automatic control, AC-45, 1131-1143.
  8. Yao, D., Zhang, S., Zhou, X. (2001). Stochastic linear quadratic control via semidefinite programming. SIAM Journal Control Optimization, 49,(3), 801-823.
  9. Yao, D., Zhang, S., Zhou, X. (2006). Tracking a financial benchmark using a few assets. Operation Research, 54,(2), 232-246.
  10. Zhou, X. & Li, D., (2000). Continuous time mean-variance portfolio selection: A stochastic LQ framework. Applied Math. Optimization, 42, 19-33.