Utility maximization in incomplete markets

By Ying Hu, Peter Imkeller, Matthias A. Muller. 2005

479 citations recorded by the source corpus.

We consider the problem of utility maximization for small traders on incomplete financial markets. As opposed to most of the papers dealing with this subject, the investors' trading strategies we allow underly constraints described by closed, but not necessarily convex, sets. The final wealths obtained by trading under these constraints are identified as stochastic processes which usually are supermartingales, and even martingales for particular strategies. These strategies are seen to be optimal, and the corresponding value functions determined simply by the initial values of the supermartingales. We separately treat the cases of exponential, power and logarithmic utility.

Subfields: Finance, Management Science and Operations Research

View Paper: https://www.semanticscholar.org/paper/2a0e9707ec1b6e987069f62888d2e2aa69b02694

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In Management Science and Operations Research

Citations in the corpus

Monotone stability of quadratic semimartingales with applications to unbounded general quadratic BSDEs (2011, background): “Some other authors have obtained further results in some particular situations (see for instance Hu & Schweizer [28], Hu, Imkeller & Muller[27], Mania and Tevzadze [36] or Delbaen, Hu & Richou [13]).”
Forward-backward systems for expected utility maximization (2011, methodology): “With this we also extend the fully stochastic approach of [14] of the optimization problem with terminal liability by means of a direct translation of martingale optimality into stochastic equations.”
ROBUST UTILITY MAXIMIZATION IN NONDOMINATED MODELS WITH 2BSDE: THE UNCERTAIN VOLATILITY MODEL (2015, methodology): “See Barrieu and El Karoui (2011), Briand and Hu (2006), and Hu et al. (2005) among others.”
A simple constructive approach to quadratic BSDEs with or without delay (2013, methodology): “Let us recall that the theory of BMO martingales was used for the first time in [9] in the context of BSDEs.”
Quadratic BSDEs with convex generators and unbounded terminal conditions (2007, methodology): “This observation can be used to obtain uniqueness see [ 8 ] and also other properties [1].”
Solvability of backward stochastic differential equations with quadratic growth (2007, unknown): “In the work of Hu at all [8] BMO-martingales were used for BSDE with quadratic generators in Brownian setting and in [15], [16], [17], [18], [19], [21] for BSDEs driven by martingales.”
BSDE with quadratic growth and unbounded terminal value (2005, background): “We should point out that BSDEs with quadratic growth in the variable z have found applications in control and finance, see, e.g., Bismut [Bis78], El Karoui, Rouge [EKR00], Hu, Imkeller, Muller [ HIM05 ], ... All the results on BSDEs with quadratic growth require that the terminal condition � is a bo”
Exponential Utility Maximization in an Incomplete Market with Defaults (2011, background): “One could think to use a verification theorem as the on of [18], but it is no longer possible since there is no existence and uniqueness results for the associated BSDE because of the presence of jumps.”
Stochastic control under progressive enlargement of filtrations and applications to multiple defaults risk management (2010, methodology): “5) This problem was addressed by several methods in the literature, and we know from dynamic programming and BSDE methods (see [22] or [8])) that V H 1 (x, θ, e) = U (”
7 – Backward Stochastic Differential Equations (2011, unknown): “[45], equilibrium pricing in incomplete market by Cheridito er al [16], the construction of gamma martingale by Darling [25], and so on.”
Harmonic analysis of stochastic equations and backward stochastic differential equations (2008, result): “Later, such kind of results are widely obtained and used, among others, by Hu, Imkeller, and Müller [26], Hu and Zhou [28], Barrieu and El Karoui [2], Briand and Hu [6, 7], and Hu et al.”
ON A NEW PARADIGM OF OPTIMAL REINSURANCE: A STOCHASTIC STACKELBERG DIFFERENTIAL GAME BETWEEN AN INSURER AND A REINSURER (2018, methodology): “In the finance and insurance literature, the BSDE approach is a useful technique to solve utility maximization problems with random parameters (see Hu et al. (2005), Shen and Wei (2016), and the references therein).”