scholarly journals Portfolio optimization under dynamic risk constraints: Continuous vs. discrete time trading

2018 ◽  
Vol 35 (1-2) ◽  
pp. 1-21
Author(s):  
Imke Redeker ◽  
Ralf Wunderlich

AbstractWe consider an investor facing a classical portfolio problem of optimal investment in a log-Brownian stock and a fixed-interest bond, but constrained to choose portfolio and consumption strategies that reduce a dynamic shortfall risk measure. For continuous- and discrete-time financial markets we investigate the loss in expected utility of intermediate consumption and terminal wealth caused by imposing a dynamic risk constraint. We derive the dynamic programming equations for the resulting stochastic optimal control problems and solve them numerically. Our numerical results indicate that the loss of portfolio performance is not too large while the risk is notably reduced. We then investigate time discretization effects and find that the loss of portfolio performance resulting from imposing a risk constraint is typically bigger than the loss resulting from infrequent trading.

2020 ◽  
Vol 23 (03) ◽  
pp. 2050017
Author(s):  
YANHONG CHEN ◽  
YIJUN HU

In this paper, we study how to evaluate the risk of a financial portfolio, whose components may be dependent and come from different markets or involve more than one kind of currencies, while we also take into consideration the uncertainty about the time value of money. Namely, we introduce a new class of risk measures, named set-valued dynamic risk measures for bounded discrete-time processes that are adapted to a given filtration. The time horizon can be finite or infinite. We investigate the representation results for them by making full use of Legendre–Fenchel conjugation theory for set-valued functions. Finally, some examples such as the set-valued dynamic average value at risk and the entropic risk measure for bounded discrete-time processes are also given.


2013 ◽  
Vol 2013 (4) ◽  
pp. 263-285 ◽  
Author(s):  
Jingzhen Liu ◽  
Ka-Fai Cedric Yiu ◽  
Tak Kuen Siu ◽  
Wai-Ki Ching

2011 ◽  
Vol 13 (8) ◽  
pp. 843-852 ◽  
Author(s):  
Stefania Guerra ◽  
Giovanni Sparacino ◽  
Andrea Facchinetti ◽  
Michele Schiavon ◽  
Chiara Dalla Man ◽  
...  

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Yinghui Dong ◽  
Wenxin Lv ◽  
Siyuan Wei ◽  
Yeyang Gong

We investigate the DC pension manager’s portfolio problem when the manager is remunerated through two schemes for DC pension managerial compensation under loss aversion and minimum guarantee. We apply the concavification technique and a static Lagrangian technique to solve the problem and derive the closed-form representation of the optimal wealth and portfolio processes. Theoretical and numerical results show that the incentive schemes can significantly impact the distribution of the optimal terminal wealth.


2010 ◽  
Vol 34 (8) ◽  
pp. 1899-1910 ◽  
Author(s):  
Olivier Brandouy ◽  
Walter Briec ◽  
Kristiaan Kerstens ◽  
Ignace Van de Woestyne

Paleobiology ◽  
2017 ◽  
Vol 43 (4) ◽  
pp. 667-692 ◽  
Author(s):  
Corentin Gibert ◽  
Gilles Escarguel

AbstractEstimating biodiversity and its variations through geologic time is a notoriously difficult task, due to several taphonomic and methodological effects that make the reconstructed signal potentially distinct from the unknown, original one. Through a simulation approach, we examine the effect of a major, surprisingly still understudied, source of potential disturbance: the effect of time discretization through biochronological construction, which generates spurious coexistences of taxa within discrete time intervals (i.e., biozones), and thus potentially makes continuous- and discrete-time biodiversity curves very different. Focusing on the taxonomic-richness dimension of biodiversity (including estimates of origination and extinction rates), our approach relies on generation of random continuous-time richness curves, which are then time-discretized to estimate the noise generated by this manipulation. A broad spectrum of data-set parameters (including average taxon longevity and biozone duration, total number of taxa, and simulated time interval) is evaluated through sensitivity analysis. We show that the deteriorating effect of time discretization on the richness signal depends highly on such parameters, most particularly on average biozone duration and taxonomic longevity because of their direct relationship with the number of false coexistences generated by time discretization. With several worst-case but realistic parameter combinations (e.g., when relatively short-lived taxa are analyzed in a long-ranging biozone framework), the original and time-discretized richness curves can ultimately show a very weak to zero correlation, making these two time series independent. Based on these simulation results, we propose a simple algorithm allowing the back-transformation of a discrete-time taxonomic-richness data set, as customarily constructed by paleontologists, into a continuous-time data set. We show that the reconstructed richness curve obtained this way fits the original signal much more closely, even when the parameter combination of the original data set is particularly adverse to an effective time-discretized reconstruction.


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