Stochastic volatility for utility maximizers — A martingale approach

2018 ◽  
Vol 05 (01) ◽  
pp. 1850007 ◽  
Author(s):  
Simon Ellersgaard ◽  
Martin Tegnér
Keyword(s):  
Stochastic Volatility ◽  
Optimal Strategies ◽  
Optimal Consumption ◽  
Investment Strategies ◽  
Relative Risk Aversion ◽  
Welfare Gains ◽  
Martingale Approach ◽  
Wealth Maximization ◽  
Heston's Model ◽  
Real Market

Using Martingale methods, we study the problem of optimal consumption-investment strategies in a complete financial market characterized by stochastic volatility. With Heston’s model as the working example, we derive optimal strategies for a constant relative risk aversion (CRRA) investor with particular attention to the cases where (i) she solely seeks to optimize her utility for consumption, and (ii) she solely seeks to optimize her bequest from investing in the market. Furthermore, we test the practical utility of our work by conducting an empirical study based on real market-data from the S&P500 index. Here, we concentrate on wealth maximization and investigate the degree to which the inclusion of derivatives facilitates higher welfare gains. Our experiments show that this is indeed the case, although we do not observe realized wealth-equivalents as high as expected. Indeed, if we factor in the increased transaction costs associated with including options, the results are somewhat less convincing.

Optimal retirement planning under partial information

2019 ◽  
Vol 36 (1-4) ◽  
pp. 37-55
Author(s):  
Nicole Bäuerle ◽  
An Chen
Keyword(s):  
Optimization Problem ◽  
Partial Information ◽  
Comparative Statics ◽  
Optimal Consumption ◽  
Investment Behavior ◽  
Martingale Method ◽  
Investment Strategies ◽  
Relative Risk Aversion ◽  
Closed Form Solutions ◽  
Optimal Consumption And Investment

Abstract The present paper analyzes an optimal consumption and investment problem of a retiree with a constant relative risk aversion (CRRA) who faces parameter uncertainty about the financial market. We solve the optimization problem under partial information by making the market observationally complete and consequently applying the martingale method to obtain closed-form solutions to the optimal consumption and investment strategies. Further, we provide some comparative statics and numerical analyses to deeply understand the consumption and investment behavior under partial information. Bearing partial information has little impact on the optimal consumption level, but it makes retirees with an RRA smaller than one invest more riskily, while it makes retirees with an RRA larger than one invest more conservatively.

OPTIMAL ENERGY DESIGN AND RETROFIT RECOMMENDATIONS FOR THE TURKISH BUILDING SECTOR

2021 ◽  
Vol 16 (1) ◽  
pp. 61-90
Author(s):  
Selçuk Sayin ◽  
Godfried Augenbroe
Keyword(s):  
Energy Saving ◽  
Large Scale ◽  
Optimal Strategies ◽  
Energy Performance ◽  
Optimization Approach ◽  
Investment Strategies ◽  
Single Family ◽  
Building Sector ◽  
Design Standards ◽  
The Cost

ABSTRACT This paper introduces methodologies and optimal strategies to reduce the energy consumption of the building sector with the aim to reduce global energy usage of a given .region or country. Many efforts are underway to develop investment strategies for large-scale energy retrofits and stricter energy design standards for existing and future buildings. This paper presents a study that informs these strategies in a novel way. It introduces support for the cost-optimized retrofits of existing, and design improvements of new buildings in Turkey with the aim to offer recommendations to individual building owners as well as guidance to the market. Three building types, apartment, single-family house and office are analyzed with a novel optimization approach. The energy performance of each type is simulated in five different climate regions of Turkey and four different vintages. For each vintage, the building is modelled corresponding to local Turkish regulations that applied at the time of construction. Optimum results are produced for different goals in terms of energy saving targets. The optimization results reveal that a 50% energy saving target is attainable for the retrofit and a 40% energy saving target is attainable for new design improvements for each building type in all climate regions.

Portfolio Optimization in Incomplete Markets

2019 ◽  
pp. 426-435
Author(s):  
Tomas Björk
Keyword(s):  
Portfolio Optimization ◽  
Incomplete Markets ◽  
Duality Theory ◽  
Optimal Investment ◽  
Optimal Consumption ◽  
Finite Sample ◽  
Martingale Approach ◽  
Dual Approach ◽  
Full Theory ◽  
Optimal Investment Problem

The object of this chapter is to give an overview of the dual approach to portfolio optimization in incomplete markets. The main result of this theory is that to every optimal investment problem there is a dual problem where we minimize a dual objective function over the class of martingale measures. For the case of a finite sample space we can present the full theory, but for the general case we only outline the proof. The theory is closely connected to convex duality theory and to the martingale approach to optimal consumption/investment discussed in Chapter 27.

Order-Book Modeling and Market Making Strategies

2018 ◽  
Vol 04 (01n02) ◽  
pp. 1950003
Author(s):  
Xiaofei Lu ◽  
Frédéric Abergel
Keyword(s):  
Optimal Strategies ◽  
Limit Order Book ◽  
Point Of View ◽  
Algorithmic Trading ◽  
Practical Implementation ◽  
Order Book ◽  
Theoretical Point ◽  
Market Making ◽  
Market Participants ◽  
Real Market

Market making is one of the most important aspects of algorithmic trading, and it has been studied quite extensively from a theoretical point of view. The practical implementation of so-called “optimal strategies” however suffers from the failure of most order-book models to faithfully reproduce the behavior of real market participants. This paper is two-fold. First, some important statistical properties of order-driven markets are identified, advocating against the use of purely Markovian order-book models. Then, market making strategies are designed and their performances are compared, based on simulation as well as backtesting. We find that incorporating some simple non-Markovian features in the limit order book greatly improves the performances of market making strategies in a realistic context.

scholarly journals State-Dependent Utility

2009 ◽  
Vol 46 (1) ◽  
pp. 55-70 ◽  
Author(s):  
Jaime A. Londoño
Keyword(s):  
General Setting ◽  
Optimal Consumption ◽  
Investment Strategies ◽  
Economic Agents ◽  
State Dependent ◽  
Portfolio Problem ◽  
Functional Forms ◽  
Secondary Result ◽  
The One ◽  
Optimal Consumption And Investment

We propose a new approach to utilities in (state) complete markets that is consistent with state-dependent utilities. Full solutions of the optimal consumption and portfolio problem are obtained in a very general setting which includes several functional forms for utilities used in the current literature, and consider general restrictions on allowable wealths. As a secondary result, we obtain a suitable representation for straightforward numerical computations of the optimal consumption and investment strategies. In our model, utilities reflect the level of consumption satisfaction of flows of cash in future times as they are (uniquely) valued by the market when the economic agents are making their consumption and investment decisions. The theoretical framework used for the model is the one proposed in Londoño (2008). We develop the martingale methodology for the solution of the problem of optimal consumption and investment in this setting.

An optimal consumption model with stochastic volatility

2003 ◽  
Vol 7 (2) ◽  
pp. 245-262 ◽  
Author(s):  
Wendell H. Fleming ◽  
Daniel Hernández-Hernández
Keyword(s):  
Stochastic Volatility ◽  
Optimal Consumption ◽  
Consumption Model

LOCAL STOCHASTIC VOLATILITY WITH JUMPS: ANALYTICAL APPROXIMATIONS

2013 ◽  
Vol 16 (08) ◽  
pp. 1350050 ◽  
Author(s):  
STEFANO PAGLIARANI ◽  
ANDREA PASCUCCI
Keyword(s):  
Characteristic Function ◽  
Stochastic Volatility ◽  
Fourier Space ◽  
Stochastic Volatility Models ◽  
Fourier Methods ◽  
Analytical Approximations ◽  
Volatility Models ◽  
Approximation Formulas ◽  
Real Market ◽  
Lévy Jumps

We present new approximation formulas for local stochastic volatility models, possibly including Lévy jumps. Our main result is an expansion of the characteristic function, which is worked out in the Fourier space. Combined with standard Fourier methods, our result provides efficient and accurate formulas for the prices and the Greeks of plain vanilla options. We finally provide numerical results to illustrate the accuracy with real market data.

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