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The price of liquidity in the reinsurance of fund returns 基金收益再保险中流动性的价格
arXiv: Mathematical Finance Pub Date : 2020-11-26 DOI: 10.21314/JOIS.2021.004
D. Saunders, L. Seco, M. Senn
{"title":"The price of liquidity in the reinsurance of fund returns","authors":"D. Saunders, L. Seco, M. Senn","doi":"10.21314/JOIS.2021.004","DOIUrl":"https://doi.org/10.21314/JOIS.2021.004","url":null,"abstract":"This paper aims to extend downside protection to a hedge fund investment portfolio based on shared loss fee structures that have become increasing popular in the market. In particular, we consider a second tranche and suggest the purchase of an upfront reinsurance contract for any losses on the fund beyond the threshold covered by the first tranche, i.e. gaining full portfolio protection. We identify a fund's underlying liquidity as a key parameter and study the pricing of this additional reinsurance using two approaches: First, an analytic closed-form solution based on the Black-Scholes framework and second, a numerical simulation using a Markov-switching model. In addition, a simplified backtesting method is implemented to evaluate the practical application of the concept.","PeriodicalId":385109,"journal":{"name":"arXiv: Mathematical Finance","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133828355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Multi-asset generalized variance swaps in Barndorff-Nielsen and Shephard model Barndorff-Nielsen和Shephard模型中的多资产广义方差互换
arXiv: Mathematical Finance Pub Date : 2020-11-26 DOI: 10.1142/s2424786320500516
Subhojit Biswas, Diganta Mukherjee, I. Sengupta
{"title":"Multi-asset generalized variance swaps in Barndorff-Nielsen and Shephard model","authors":"Subhojit Biswas, Diganta Mukherjee, I. Sengupta","doi":"10.1142/s2424786320500516","DOIUrl":"https://doi.org/10.1142/s2424786320500516","url":null,"abstract":"This paper proposes swaps on two important new measures of generalized variance, namely the maximum eigenvalue and trace of the covariance matrix of the assets involved. We price these generalized variance swaps for Barndorff-Nielsen and Shephard model used in financial markets. We consider multiple assets in the portfolio for theoretical purpose and demonstrate our approach with numerical examples taking three stocks in the portfolio. The results obtained in this paper have important implications for the commodity sector where such swaps would be useful for hedging risk.","PeriodicalId":385109,"journal":{"name":"arXiv: Mathematical Finance","volume":"75 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121091508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Dual Characterisation of Regulatory Arbitrage for Coherent Risk Measures 一致性风险测度的监管套利的双重特征
arXiv: Mathematical Finance Pub Date : 2020-09-11 DOI: 10.2139/ssrn.3691027
Martin Herdegen, Nazem Khan
{"title":"A Dual Characterisation of Regulatory Arbitrage for Coherent Risk Measures","authors":"Martin Herdegen, Nazem Khan","doi":"10.2139/ssrn.3691027","DOIUrl":"https://doi.org/10.2139/ssrn.3691027","url":null,"abstract":"We revisit mean-risk portfolio selection in a one-period financial market where risk is quantified by a positively homogeneous risk measure $rho$ on $L^1$. We first show that under mild assumptions, the set of optimal portfolios for a fixed return is nonempty and compact. However, unlike in classical mean-variance portfolio selection, it can happen that no efficient portfolios exist. We call this situation regulatory arbitrage, and prove that it cannot be excluded - unless $rho$ is as conservative as the worst-case risk measure. After providing a primal characterisation, we focus our attention on coherent risk measures, and give a necessary and sufficient characterisation for regulatory arbitrage. We show that the presence or absence of regulatory arbitrage for $rho$ is intimately linked to the interplay between the set of equivalent martingale measures (EMMs) for the discounted risky assets and the set of absolutely continuous measures in the dual representation of $rho$. A special case of our result shows that the market does not admit regulatory arbitrage for Expected Shortfall at level $alpha$ if and only if there exists an EMM $mathbb{Q} approx mathbb{P}$ such that $Vert frac{text{d}mathbb{Q}}{text{d}mathbb{P}} Vert_{infty} < frac{1}{alpha}$.","PeriodicalId":385109,"journal":{"name":"arXiv: Mathematical Finance","volume":"100 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127165286","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Pseudo-Hermiticity and Removing Brownian Motion From Finance 伪厄米性与从金融学中剔除布朗运动
arXiv: Mathematical Finance Pub Date : 2020-09-01 DOI: 10.2139/ssrn.3684508
William Hicks
{"title":"Pseudo-Hermiticity and Removing Brownian Motion From Finance","authors":"William Hicks","doi":"10.2139/ssrn.3684508","DOIUrl":"https://doi.org/10.2139/ssrn.3684508","url":null,"abstract":"In this article we apply the methods of quantum mechanics to the study of the financial markets. Specifically, we discuss the Pseudo-Hermiticity of the Hamiltonian operators associated to the typical partial differential equations of Mathematical Finance (such as the Black-Scholes equation) and how this relates to the non-arbitrage condition. \u0000We propose that one can use a Schrodinger equation to derive the probabilistic behaviour of the financial market, and discuss the benefits of doing so. This presents an alternative approach to replace the use of standard diffusion processes (for example a Brownian motion or Wiener process). \u0000We go on to study the method using the Bohmian approach to quantum mechanics. We consider how to interpret the equations for pseudo-Hermitian systems, and highlight the crucial role played by the quantum potential function.","PeriodicalId":385109,"journal":{"name":"arXiv: Mathematical Finance","volume":"50 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116062130","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
A pure-jump mean-reverting short rate model 纯跳跃均值回归短期利率模型
arXiv: Mathematical Finance Pub Date : 2020-04-20 DOI: 10.15559/20-VMSTA152
M. Hess
{"title":"A pure-jump mean-reverting short rate model","authors":"M. Hess","doi":"10.15559/20-VMSTA152","DOIUrl":"https://doi.org/10.15559/20-VMSTA152","url":null,"abstract":"A new multi-factor short rate model is presented which is bounded from below by a real-valued function of time. The mean-reverting short rate process is modeled by a sum of pure-jump Ornstein--Uhlenbeck processes such that the related bond prices possess affine representations. Also the dynamics of the associated instantaneous forward rate is provided and a condition is derived under which the model can be market-consistently calibrated. The analytical tractability of this model is illustrated by the derivation of an explicit plain vanilla option price formula. With view on practical applications, suitable probability distributions are proposed for the driving jump processes. The paper is concluded by presenting a post-crisis extension of the proposed short and forward rate model.","PeriodicalId":385109,"journal":{"name":"arXiv: Mathematical Finance","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131407563","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
A note on the worst case approach for a market with a stochastic interest rate. 关于随机利率市场的最坏情况方法的说明。
arXiv: Mathematical Finance Pub Date : 2020-01-07 DOI: 10.4064/am2348-2-2018
Dariusz Zawisza
{"title":"A note on the worst case approach for a market with a stochastic interest rate.","authors":"Dariusz Zawisza","doi":"10.4064/am2348-2-2018","DOIUrl":"https://doi.org/10.4064/am2348-2-2018","url":null,"abstract":"We solve robust optimization problem and show the example of the market model for which the worst case measure is not a martingale measure. In our model the instantaneous interest rate is determined by the Hull-White model and the investor employs the HARA utility to measure his satisfaction.To protect against the model uncertainty he uses the worst case measure approach. The problem is formulated as a stochastic game between the investor and the market from the other side. PDE methods are used to find the saddle point and the precise verification argument is provided.","PeriodicalId":385109,"journal":{"name":"arXiv: Mathematical Finance","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130301291","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Multi-time state mean-variance model in continuous time 连续时间多时间状态均值-方差模型
arXiv: Mathematical Finance Pub Date : 2019-12-04 DOI: 10.1051/COCV/2021086
Shuzhen Yang
{"title":"Multi-time state mean-variance model in continuous time","authors":"Shuzhen Yang","doi":"10.1051/COCV/2021086","DOIUrl":"https://doi.org/10.1051/COCV/2021086","url":null,"abstract":"In the continuous time mean-variance model, we want to minimize the variance (risk) of the investment portfolio with a given mean at terminal time. However, the investor can stop the investment plan at any time before the terminal time. To solve this kind of problem, we consider to minimize the variances of the investment portfolio at multi-time state. The advantage of this multi-time state mean-variance model is that we can minimize the risk of the investment portfolio along the investment period. To obtain the optimal strategy of the multi-time state mean-variance model, we introduce a sequence of Riccati equations which are connected by a jump boundary condition. Based on this sequence Riccati equations, we establish the relationship between the means and variances of this multi-time state mean-variance model. Furthermore, we use an example to verify that minimizing the variances of the multi-time state can affect the average of Maximum-Drawdown of the investment portfolio.","PeriodicalId":385109,"journal":{"name":"arXiv: Mathematical Finance","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114715468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
SURVIVAL INVESTMENT STRATEGIES IN A CONTINUOUS-TIME MARKET MODEL WITH COMPETITION 具有竞争的连续时间市场模型下的生存投资策略
arXiv: Mathematical Finance Pub Date : 2019-09-05 DOI: 10.1142/s0219024921500011
M. Zhitlukhin
{"title":"SURVIVAL INVESTMENT STRATEGIES IN A CONTINUOUS-TIME MARKET MODEL WITH COMPETITION","authors":"M. Zhitlukhin","doi":"10.1142/s0219024921500011","DOIUrl":"https://doi.org/10.1142/s0219024921500011","url":null,"abstract":"We consider a stochastic game-theoretic model of an investment market in continuous time with short-lived assets and study strategies, called survival, which guarantee that the relative wealth of an investor who uses such a strategy remains bounded away from zero. The main results consist in obtaining a sufficient condition for a strategy to be survival and showing that all survival strategies are asymptotically close to each other. It is also proved that a survival strategy allows an investor to accumulate wealth in a certain sense faster than competitors.","PeriodicalId":385109,"journal":{"name":"arXiv: Mathematical Finance","volume":"49 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116283014","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
CONSISTENT UPPER PRICE BOUNDS FOR EXOTIC OPTIONS 异域期权一致的价格上限
arXiv: Mathematical Finance Pub Date : 2019-07-22 DOI: 10.1142/S0219024921500114
Nicole Bauerle, Daniel Schmithals
{"title":"CONSISTENT UPPER PRICE BOUNDS FOR EXOTIC OPTIONS","authors":"Nicole Bauerle, Daniel Schmithals","doi":"10.1142/S0219024921500114","DOIUrl":"https://doi.org/10.1142/S0219024921500114","url":null,"abstract":"We consider the problem of finding a consistent upper price bound for exotic options whose payoff depends on the stock price at two different predetermined time points (e.g. Asian option), given a finite number of observed call prices for these maturities. A model-free approach is used, only taking into account that the (discounted) stock price process is a martingale under the no-arbitrage condition. In case the payoff is directionally convex we obtain the worst case marginal pricing measures. The speed of convergence of the upper price bound is determined when the number of observed stock prices increases. We illustrate our findings with some numerical computations.","PeriodicalId":385109,"journal":{"name":"arXiv: Mathematical Finance","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131542301","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Arbitrage-Free Interpolation in Models of Market Observable Interest Rates 市场可观察利率模型中的无套利插值
arXiv: Mathematical Finance Pub Date : 2018-06-21 DOI: 10.1007/978-3-662-04790-3_11
Erik Schlogl
{"title":"Arbitrage-Free Interpolation in Models of Market Observable Interest Rates","authors":"Erik Schlogl","doi":"10.1007/978-3-662-04790-3_11","DOIUrl":"https://doi.org/10.1007/978-3-662-04790-3_11","url":null,"abstract":"","PeriodicalId":385109,"journal":{"name":"arXiv: Mathematical Finance","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132587463","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 16
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