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Application of BSDE in Standard Inventory Financing Loan

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  • Hui Zhang
  • Wenyu Meng
  • Xiaojie Wang
  • Jianwei Zhang

Abstract

This paper examines the issue of loans obtained by the small and medium-sized enterprises (SMEs) from banks through the mortgage inventory of goods. And the loan-to-value (LTV) ratio which affects the loan business is a very critical factor. In this paper, we provide a general framework to determine a bank’s optimal loan-to-value (LTV) ratio when we consider the collateral value in the financial market with Knightian uncertainty. We assume that the short-term prices of the collateral follow a geometric Brownian motion. We use a set of equivalent martingale measures to build the models about a bank’s maximum and minimum levels of risk tolerance in an environment with Knightian uncertainty. The models about the LTV ratios are established with the bank’s maximum and minimum risk preferences. Applying backward stochastic differential equations (BSDEs), we get the explicit solutions of the models. Applying the explicit solutions, we can obtain an interval solution for the optimal LTV ratio. Our numerical analysis shows that the LTV ratio in the Knightian uncertainty-neutral environment belongs to the interval solutions derived from the models.

Suggested Citation

  • Hui Zhang & Wenyu Meng & Xiaojie Wang & Jianwei Zhang, 2017. "Application of BSDE in Standard Inventory Financing Loan," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-6, June.
    • Handle: RePEc:hin:jnddns:1031247
    DOI: 10.1155/2017/1031247
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    1. repec:bla:ecnote:v:32:y:2003:i:2:p:243-282 is not listed on IDEAS
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    3. N. El Karoui & S. Peng & M. C. Quenez, 1997. "Backward Stochastic Differential Equations in Finance," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 1-71, January.
    4. Yehuda Izhakian, 2012. "Capital Asset Pricing Under Ambiguity," Working Papers 12-02, New York University, Leonard N. Stern School of Business, Department of Economics.
    5. Cossin, Didier & González, Fernando & Huang, Zhijiang & Backé, Peter, 2003. "A framework for collateral risk control determination," Working Paper Series 209, European Central Bank.
    6. Esa Jokivuolle & Samu Peura, 2003. "Incorporating Collateral Value Uncertainty in Loss Given Default Estimates and Loan‐to‐value Ratios," European Financial Management, European Financial Management Association, vol. 9(3), pages 299-314, September.
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