Erratum to: Utility maximization in incomplete markets with random endowment

Continuity of Utility Maximization under Weak Convergence

“…With convergence of numerical schemes in mind, this paper deals with the following question: Given a utility function and a sequence of financial markets with underlying assets (S (n) ) n∈N that are converging weakly to S, under which conditions do the values of the utility maximization problems (from terminal wealth) converge to the corresponding value for the model given by S? Although the utility maximization problems enjoyed a considerable attention in the literature (see, for instance, [32,33,24,26,10,8,20,38,4]), to the best of our knowledge, the continuity under weak convergence was studied only in a complete market setup (see [19,37,39]). In this work we consider this convergence question for general incomplete market models and continuous (as a function of the terminal wealth) random utility functions.…”

Conditional Davis Pricing

“…that is, the restriction of v(·; B) to constant payoffs ϕ = x ∈ R can fail to be differentiable on the interior of its domain 1 . See also the discussion in Erratum [7]. an offshoot, we show additionally that the mapping ϕ → v(ϕ; B) is smooth whenever B is uniquely super-replicable.…”

“…This is the most attractive feature of our linear characterization in 4 The authors first learned from Pietro Siorpaes about the potential lack of correctness of Remark 4.2 in [6]. We also refer the reader to Erratum [7] for further discussions. Proposition 6.5 below; however, as we shall see later, it also leads to explicit computations in many cases.…”

“…that is, the restriction of v(•; B) to constant payoffs ϕ = x ∈ R can fail to be differentiable on the interior of its domain 1 . See also the discussion in Erratum [7]. (3) Under the additional assumption of unique super-replicability from [27] placed on (B, ϕ), we solve the linear stochastic control problem mentioned in (2) explicitly.…”

“…The authors first learned from Pietro Siorpaes about the potential lack of correctness of Remark 4.2 in[6]. We also refer the reader to Erratum[7] for further discussions.…”