Systemic risk with relative behavior

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姓名

林志剛(Chih-Kang Lin) 查詢紙本館藏

畢業系所

統計研究所

論文名稱

(Systemic risk with relative behavior)

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摘要(中)

本文中，我們探討當企業間互相影響而做出不同的借貸策略。一開始我們考慮兩間異質的銀行，為了找出一最佳化策略使得某家銀行在向另一家銀行借貸時花費最小的成本，若我們的資產額低於對手則向他借錢，相反地若我們的資產額高於對手時則放款給他，我們利用Hamilton-Jacobi-Bellman(HJB)方程式去找出奈許均衡點。第二部份我們討論同質的N家銀行，一樣藉由HJB方程式來找出奈許均衡點並觀察相對表現的比值如何影響存活機率。

摘要(英)

In this paper, we consider the problem of optimal lending and borrowing where executives take into account the relative to their peers. First, we study two heterogeneous banks. In order to find the optimal strategy through minimizing the quadratic cost for borrowing or lending and an intention to borrow if the capital is low or lend if the capital is high by comparison to the fund of opponent, we use the Hamilton-Jacobi-Bellman(HJB) equations to obtain the Nash equilibrium. Second, the case of $N$ homogeneous banks is discussed. We obtain the Nash equilibrium by using the HJB equations and observe the influence of the ratio of relative performance on the survival probability.

關鍵字(中)

★ HJB方程式
★ 奈許均衡點
★ 最佳化策略
★ 成本最小化

關鍵字(英)

★ HJB equation
★ Nash equilibrium
★ optimal strategy
★ minimize the cost

論文目次

摘要 i
Abstract ii
誌謝 iii
1 introduction 1
2 Two heterogeneous banks 4
2.1 Model 4
2.2 Financial Implications 6
3 N homogeneous banks 9
3.1 Stability and Systemic Risk 9
3.2 Model with controls 12
3.3 Financial Implication 15
4 Conclusion 17
Appendices 18
References 32

參考文獻

R. Carmona, J.-P. Fouque, M. Mousafa, and L.-H. Sun. Systemic risk and stochastic games
with delay. arXiv:1607.06373.
R. Carmona, J.-P. Fouque, and L.-H. Sun. (2015) Mean field games and systemic risk. Communi-
cations in Mathematical Sciences, 13(4):911–933.
G.-E. Espinosa and N. Touzi. (2015) Optimal investment under relative performance concerns.\r Mathematical Finance, 25(2):221–257.
J.-P. Fouque and L.-H. Sun. (2013) Systemic risk illustrated. Handbook on Systemic Risk, Eds
J.-P. Fouque and J. Langsam.

指導教授

孫立憲(Li-Hsien Sun)

審核日期

2017-7-27

推文