Upper Envelopes of Families of Feller Semigroups and Viscosity Solutions to a Class of Nonlinear Cauchy Problems Read More: https://epubs.siam.org/doi/10.1137/20M1314823
Nendel M, Röckner M (2021)
SIAM Journal on Control and Optimization 59(6): 4400-4428.
Zeitschriftenaufsatz
| Veröffentlicht | Englisch
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Einrichtung
Abstract / Bemerkung
In this paper, we consider the (upper) semigroup envelope, i.e., the least upper bound, of a given family of linear Feller semigroups. We explicitly construct the semigroup envelope and show that, under suitable assumptions, it yields viscosity solutions to abstract HJB-type PDEs related to stochastic optimal control problems arising in the field of robust finance. We further derive conditions for the existence of a Markov process under a nonlinear expectation related to the semigroup envelope for the case where the state space is locally compact. The procedure is then applied to numerous examples, in particular, nonlinear PDEs that arise from control problems for infinite-dimensional Ornstein-Uhlenbeck and Le ' vy processes.
Stichworte
semigroup envelope;
fully nonlinear PDE;
viscosity solution;
Feller;
process;
model uncertainty;
nonlinear expectation
Erscheinungsjahr
2021
Zeitschriftentitel
SIAM Journal on Control and Optimization
Band
59
Ausgabe
6
Seite(n)
4400-4428
ISSN
0363-0129
eISSN
1095-7138
Page URI
https://pub.uni-bielefeld.de/record/2960405
Zitieren
Nendel M, Röckner M. Upper Envelopes of Families of Feller Semigroups and Viscosity Solutions to a Class of Nonlinear Cauchy Problems Read More: https://epubs.siam.org/doi/10.1137/20M1314823. SIAM Journal on Control and Optimization. 2021;59(6):4400-4428.
Nendel, M., & Röckner, M. (2021). Upper Envelopes of Families of Feller Semigroups and Viscosity Solutions to a Class of Nonlinear Cauchy Problems Read More: https://epubs.siam.org/doi/10.1137/20M1314823. SIAM Journal on Control and Optimization, 59(6), 4400-4428. https://doi.org/10.1137/20M1314823
Nendel, Max, and Röckner, Michael. 2021. “Upper Envelopes of Families of Feller Semigroups and Viscosity Solutions to a Class of Nonlinear Cauchy Problems Read More: https://epubs.siam.org/doi/10.1137/20M1314823”. SIAM Journal on Control and Optimization 59 (6): 4400-4428.
Nendel, M., and Röckner, M. (2021). Upper Envelopes of Families of Feller Semigroups and Viscosity Solutions to a Class of Nonlinear Cauchy Problems Read More: https://epubs.siam.org/doi/10.1137/20M1314823. SIAM Journal on Control and Optimization 59, 4400-4428.
Nendel, M., & Röckner, M., 2021. Upper Envelopes of Families of Feller Semigroups and Viscosity Solutions to a Class of Nonlinear Cauchy Problems Read More: https://epubs.siam.org/doi/10.1137/20M1314823. SIAM Journal on Control and Optimization, 59(6), p 4400-4428.
M. Nendel and M. Röckner, “Upper Envelopes of Families of Feller Semigroups and Viscosity Solutions to a Class of Nonlinear Cauchy Problems Read More: https://epubs.siam.org/doi/10.1137/20M1314823”, SIAM Journal on Control and Optimization, vol. 59, 2021, pp. 4400-4428.
Nendel, M., Röckner, M.: Upper Envelopes of Families of Feller Semigroups and Viscosity Solutions to a Class of Nonlinear Cauchy Problems Read More: https://epubs.siam.org/doi/10.1137/20M1314823. SIAM Journal on Control and Optimization. 59, 4400-4428 (2021).
Nendel, Max, and Röckner, Michael. “Upper Envelopes of Families of Feller Semigroups and Viscosity Solutions to a Class of Nonlinear Cauchy Problems Read More: https://epubs.siam.org/doi/10.1137/20M1314823”. SIAM Journal on Control and Optimization 59.6 (2021): 4400-4428.
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