Buy and hold golden strategies in financial markets with frictions and depth constraints. (English) Zbl 07878240
Summary: This paper deals with coherent risk measures and golden strategies, that is, financial portfolios (or financial strategies) with a negative risk and a non positive price. Golden strategies are important because they enable us to outperform every portfolio in a return/risk approach. In fact, every portfolio of securities is beaten by adding the golden strategy, i.e., the portfolio plus the golden strategy is better than the portfolio alone. Computationally tractable algorithms will be presented, and the general framework will be very realistic. Indeed, the study will incorporate all the classical frictions provoked by the order book of a financial market, and it will be both buy-and-hold and model-free. Numerical experiments involving derivative markets will be analysed.
Software:
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| [1] | Ahn, D., Boudoukh, J., Richardson, M., and Whitelaw, R. F.. 1999. “Optimal Risk Management Using Options.” The Journal of Finance54 (1): 359-375. . |
| [2] | Anderson, E. J., and Nash, P.. 1987. Linear Programming in Infinite Dimensional Spaces. Hoboken, NJ: John Wiley & Sons. · Zbl 0632.90038 |
| [3] | Artzner, P., Delbaen, F., Eber, J. M., and Health, D.. 1999. “Coherent Measures of Risk.” Mathematical Finance9 (3): 203-228. . · Zbl 0980.91042 |
| [4] | Balbás, A., Balbás, B., and Balbás, R.. 2010. “CAPM and APT-Like Models with Risk Measures.” Journal of Banking & Finance34 (6): 1166-1174. . |
| [5] | Balbás, A., Balbás, B., and Balbás, R.. 2016a. “Outperforming Benchmarks with Their Derivatives: Theory and Empirical Evidence.” Journal of Risk18 (4): 25-52. . |
| [6] | Balbás, A., Balbás, B., and Balbás, R.. 2016b. “Good Deals and Benchmarks in Robust Portfolio Selection.” European Journal of Operational Research250 (2): 666-678. . · Zbl 1346.91198 |
| [7] | Balbás, A., Balbás, B., and Balbás, R.. 2019. “Golden Options in Financial Mathematics.” Mathematics and Financial Economics13 (4): 637-659. . · Zbl 1422.91679 |
| [8] | Balbás, A., Balbás, B., and Balbás, R.. 2022. “Pareto Efficient Buy and Hold Investment Strategies under Order Book Linked Constraints.” Annals of Operations Research311 (2): 945-965. . · Zbl 1490.91180 |
| [9] | Balbás, A., Balbás, B., Balbás, R., and Charron, J. P.. 2023. “Bidual Representation of Expectiles.” Risks11 (12): 220. . |
| [10] | Balbás, A., and Serna, G.. 2024. “Selling Options to Beat the Market: Further Empirical Evidence.” Research in International Business and Finance67:102119. . |
| [11] | Bondarenko, O.2014. “Why are Put Options so Expensive?” Quarterly Journal of Finance4 (3): 1450015. . |
| [12] | Cheung, K. C., Chong, W. F., and Lo, A.. 2019. “Budget-Constrained Optimal Reinsurance Design under Coherent Risk Measure.” Scandinavian Actuarial Journal2019 (9): 729-751. . · Zbl 1426.91209 |
| [13] | Constantinides, G. M., Czerwonko, M., Jackwerth, J. C., and Perrakis, S.. 2011. “Are Options on Index Futures Profitable for Risk-Averse Investors? Empirical Evidence.” The Journal of Finance66 (4): 1407-1437. . |
| [14] | Cui, J., Liao, C., Ji, L., Xie, Y., Yu, Y., and Yin, J.. 2021. “A Short-Term Hybrid Energy System Robust Optimization Model for Regional Electric-Power Capacity Development Planning Under Different Pollutant Control Pressures.” Sustainability13 (20): 11341. . |
| [15] | Delbaen, F.2013. A Remark on the Structure of Expectiles. Preprint, arXiv: 1307.5881v1. |
| [16] | Dupacová, J., and Kopa, M.. 2014. “Robustness of Optimal Portfolios under Risk and Stochastic Dominance Constraints.” European Journal of Operational Research234 (2): 434-441. . · Zbl 1304.91190 |
| [17] | Filippi, C., Guastaroba, G., and Speranza, M. G.. 2020. “Conditional Value-at-Risk Beyond Finance: A Survey.” International Transactions in Operational Research27 (3): 1273-1814. . |
| [18] | Goovaerts, J. M., and Laeven, R.. 2008. “Actuarial Risk Measures for Financial Derivative Pricing.” Insurance: Mathematics and Economics42 (2): 540-547. · Zbl 1152.91444 |
| [19] | Hamada, M., and Sherris, M.. 2003. “Contingent Claim Pricing Using Probability Distortion Operators: Method from Insurance Risk Pricing and Their Relationship to Financial Theory.” Applied Mathematical Finance10 (1): 19-47. . · Zbl 1064.91043 |
| [20] | Haugh, M. B., and Lo, A. W.. 2001. “Asset Allocation and Derivatives.” Quantitative Finance1 (1): 45-72. . · Zbl 1405.91694 |
| [21] | Jiekang, W., Zhijiang, W, Xiaoming, M., Fan, W., Huiling, T., and Lingming, C.. 2020. “Risk Early Warning Method for Distribution System with Sources-Networks-Loads-Vehicles Based on Fuzzy C-Mean Clustering.” Electric Power Systems Research180:106059. . |
| [22] | Jin, H., and Zhou, X. Y.. 2008. “Behavioral Portfolio Selection in Continuous Time.” Mathematical Finance18 (3): 385-426. . · Zbl 1141.91454 |
| [23] | Johnston, M.2009. “Extending the Basel II Approach to Estimate Capital Requirements for Equity Investments.” Journal of Banking & Finance33 (6): 1177-1185. . |
| [24] | Jouini, E., and Kallal, H.. 1995. “Martingales and Arbitrage in Securities Markets with Transaction Costs.” Journal of Economic Theory66 (1): 178-197. . · Zbl 0830.90020 |
| [25] | Kim, J. H.2007. “Risk Measure Pricing and Hedging in the Presence of Transaction Costs.” Journal of Applied Mathematics and Computing23 (1-2): 293-310. . · Zbl 1210.91059 |
| [26] | Lejeune, M., and Shen, S.. 2016. “Multi-Objective Probabilistically Constrained Programs with Variable Risk: Models for Multi-Portfolio Financial Optimization.” European Journal of Operational Research252 (2): 522-539. . · Zbl 1346.91212 |
| [27] | Lia, D., Zeng, Y., and Yang, H.. 2018. “Robust Optimal Excess-of-Loss Reinsurance and Investment Strategy for an Insurer in a Model with Jumps.” Scandinavian Actuarial Journal2018 (2): 145-171. . · Zbl 1416.91203 |
| [28] | Luenberger, D. G.1969. Optimization by Vector Spaces Methods. New York: John Wiley & Sons. · Zbl 0176.12701 |
| [29] | Luenberger, D. G.2001. “Projection Pricing.” Journal of Optimization Theory and Applications109 (1): 1-25. . · Zbl 0972.91058 |
| [30] | Morón, M. A., Romero, C., and Ruiz, F. R.. 1996. “Generating Well-Behaved Utility Functions for Compromise Programming.” Journal of Optimization Theory and Applications91 (3): 643-649. . · Zbl 0866.90105 |
| [31] | Nakano, Y.2004. “Efficient Hedging with Coherent Risk Measure.” Journal of Mathematical Analysis and Applications293 (1): 345-354. . · Zbl 1085.91032 |
| [32] | Newey, W., and Powell, J.. 1987. “Asymmetric Least Squares Estimation and Testing.” Econometrica55 (4): 819-847. . · Zbl 0625.62047 |
| [33] | Rockafellar, R. T., Uryasev, S., and Zabarankin, M.. 2006. “Generalized Deviations in Risk Analysis.” Finance & Stochastics10 (1): 51-74. . · Zbl 1150.90006 |
| [34] | Stoyanov, S. V., Rachev, S. T., and Fabozzi, F. J.. 2007. “Optimal Financial Portfolios.” Applied Mathematical Finance14 (5): 401-436. . · Zbl 1151.91542 |
| [35] | Tadese, M., and Drapeau, S.. 2020. “Relative Bound and Asymptotic Comparison of Expectile with Respect to Expected Shortfall.” Insurance: Mathematics and Economics93:387-399. · Zbl 1448.62064 |
| [36] | Tapiero, C.2004. Risk and Financial Management: Mathematical and Computational Methods. Chichester: John Wiley. · Zbl 1103.91003 |
| [37] | Wu, J., Wu, Z., Wu, F., Tang, H., and Mao, X.. 2018. “CVaR Risk-Based Optimization Framework for Renewable Energy Management in Distribution Systems with DGs and EVs.” Energy143:323-336. . |
| [38] | Zeidler, E.1995. Applied Functional Analysis: Main Principles and Their Applications. New York: Springer. · Zbl 0834.46003 |
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