LUISS

List of Publications

List of Publications of Fausto Gozzi

Book

Stochastic Optimal Control in Infinite Dimensions: Dynamic Programming and HJB Equations, G. Fabbri, F. Gozzi and A. Swiech, with Chapter 6 by M. Fuhrman and G. Tessitore;

Here you find Chapters 1-3, the Appendix and an Erratum file.

The book has been recently published  in Springer series on “Probability Theory and Stochastic Modelling”, Vol 82, (2017).

 

Recent working papers

      1. BOUCEKKINE R., FABBRI G., FEDERICO S., GOZZI F. (2017). Growth and Agglomeration in the Heterogeneous Space: A Generalized AK Approach. Submitted. Preprint.
      2. GOZZI F., MONTE R., TESSITORE M.E. (2017). On the dynamic programming approach for incentive constrained problems. Submitted. Preprint
      3. FEDERICO S., GOZZI F. (2017). Verification theorems for stochastic optimal control problems in Hilbert spaces by means of a generalized Dynkin formula. Submitted. Preprint.
      4. ACQUISTAPACE P., GOZZI F. (2016). Minimum energy for linear systems with finite horizon: a non-standard Riccati equation. Submitted. Preprint.

 

Papers in refereed international journals

      1. FRENI G, GOZZI F., SALVADORI N (2017). Existence of optimal strategies in linear multisector models with several consumption goods. DECISIONS IN ECONOMICS AND FINANCE (to appear). Preprint.
      2. GOZZI F., MASIERO F. (2017).  Stochastic Optimal Control with Delay in the Control I: solution through partial smoothing. SIAM JOURNAL ON CONTROL AND OPTIMIZATION (to appear). Preprint.
      3. GOZZI F., MASIERO F. (2017).  Stochastic Optimal Control with Delay in the Control II: Verification Theorem and Optimal Feedbacks. SIAM JOURNAL ON CONTROL AND OPTIMIZATION (to appear). Preprint.
      4. COSSO A., FEDERICO S., GOZZI F., ROSESTOLATO M., TOUZI N. (2017). Path-dependent equations and viscosity solutions in infinite dimension. ANNALS OF PROBABILITY (to appear). Preprint.
      5. AUGERAUD-VERON E., BAMBI M., GOZZI F. (2017). On the equivalence of internal and external habit formation models with finite memory, JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS (to appear). Preprint.
      6. BAMBI M., DI GIROLAMI C., FEDERICO S., GOZZI F. (2017).  Generically distributed investments on flexible projects and endogenous growth. ECONOMIC THEORY, Volume 63, Issue 2, (February 2017), 521–558. Preprint.
      7. FEDERICO S., GOZZI F. (2016). Mild solutions of semilinear elliptic equations in Hilbert spaces. JOURNAL OF DIFFERENTIAL EQUATIONS Volume 262, Issue 5, p. 3343-3389. Preprint.
      8. FEDERICO S., GASSIAT P., GOZZI F. (2015). Impact of time illiquidity in a mixed market without full observation.  MATHEMATICAL FINANCE (to appear). Preprint.
      9. FEDERICO S., GASSIAT P., GOZZI F. (2015). Utility maximization with current utility on the wealth: regularity of solutions to the HJB equation. FINANCE AND STOCHASTICS 19 (No 2) 415-448. Preprint.
      10. BOUCEKKINE R., FABBRI G., GOZZI F. (2014). Egalitarianism under population change: age structure does matter. JOURNAL OF MATHEMATICAL ECONOMICS, Volume 55, December 2014, Pages 86-100. Preprint.
      11. BAMBI M., GOZZI F., LICANDRO O. (2014). Endogenous Growth and Wave-like Business Fluctuations. JOURNAL OF ECONOMIC THEORY 154, 68-111. Preprint.
      12. GASSIAT P., GOZZI F., PHAM H. (2014). Investment/consumption problem in illiquid markets with regime-switching. SIAM JOURNAL ON CONTROL AND OPTIMIZATION  vol 52(3), 1761-1786. Preprint.
      13. DI GIACINTO M., FEDERICO S., GOZZI F., VIGNA E. (2014). Income drawdown Option with Minimum Guarantees. EUROPEAN J. OF OPERATION RESEARCH Vol. 234, No. 3, 610-624. Preprint.
      14. BAMBI M, FABBRI G, GOZZI F. (2012). Optimal policy and consumption smoothing effects in the time-to-build AK model. ECONOMIC THEORY, 50 (3), p635-669.Preprint
      15. BOUCEKKINE R., FABBRI G., GOZZI F. (2011). Revisiting the optimal population size problem under endogenous growth: Minimal utility level and finite life. ASIA-PACIFIC JOURNAL OF ACCOUNTING & ECONOMICS, Vol. 18 (3), pp 287-306.  WP version.
      16. FEDERICO S, GOLDYS B, GOZZI F. (2011). HJB Equations for the Optimal Control of Differential Equations with Delays and State Constraints, II: Optimal Feedbacks and Approximations. SIAM JOURNAL ON CONTROL AND OPTIMIZATION Vol. 49, pp. 2378-2414.  Working paper version in ARXIV.
      17. DI GIACINTO M, FEDERICO S, GOZZI F. (2011). Pension Funds with a Minimum Guarantee: A Stochastic Control Approach. FINANCE AND STOCHASTICS, Volume 15, Number 2, Pages 297-342. Working paper version in SSRN.
      18. CRETAROLA A, GOZZI F., PHAM H, TANKOV P (2011). Optimal consumption in illiquid markets. FINANCE AND STOCHASTICS, Volume 15, Number 1, Pages 85-115. Working paper version in ARXIV.
      19. BOUCEKKINE R., FABBRI G., GOZZI F. (2010). Maintenance and Investment: Complements or Substitutes? A Reappraisal. JOURNAL OF ECONOMIC DYNAMICS & CONTROL, 34(12); p 2420-2439. pdf
      20. FAGGIAN S, GOZZI F. (2010). Dynamic programming for infinite horizon boundary control problems of PDE’s with age structure. JOURNAL OF MATHEMATICAL ECONOMICS, 46 (4), pp. 416-437. pdf
      21. FEDERICO S, GOLDYS B, GOZZI F. (2010). HJB Equations for the Optimal Control of DDEs with State Constraints: Regularity of Viscosity Solutions. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 48, pp. 4910-4937. pdf
      22. GOZZI F., SWIECH A, ZHOU X.Y (2010). Erratum to “A corrected proof of the stochastic veri cation theorem within the framework of viscosity solutions”. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 48, pp. 4177-4179.pdf
      23. FABBRI G, GOZZI F., SWIECH A (2010). Verification theorem and construction of epsilon-optimal controls for control of abstract evolution equations. JOURNAL OF CONVEX ANALYSIS, 17(2); p 611-642. pdf
      24. GOZZI F., MARINELLI C, SAVIN S (2009). Optimal advertising under uncertainty with carryover effects. JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, Volume 142, Number 2, 291-321.pdf
      25. FABBRI G, GOZZI F. (2008). Solving optimal growth models with vintage capital: The dynamic programming approach. JOURNAL OF ECONOMIC THEORY, vol. 143 – 1; p. 331-373. pdf
      26. FRENI G, GOZZI F., PIGNOTTI C (2008). A Multisector AK model with endogenous growth: Value function and optimality conditions. JOURNAL OF MATHEMATICAL ECONOMICS, vol. 44 (1); p. 55-86.pdf
      27. FABBRI G, FAGGIAN S, GOZZI F. (2008). On Dynamic Programming in Economic Models governed by DDE’s. MATHEMATICAL POPULATION STUDIES, vol. 15(4); p. 267-290. pdf
      28. FRENI G, GOZZI F., SALVADORI N (2006). Existence of Optimal Strategies in linear Multisector Models. ECONOMIC THEORY, vol. 29  (1); p. 25-48. pdf
      29. GOLDYS B, GOZZI F. (2006). Second order Hamilton-Jacobi-Bellman equations in Hilbert spaces and stochastic control: L2 approach. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, vol. 116; p. 1932-1963. pdf
      30. GOZZI F. (2006). Smoothing properties of nonlinear Transition Semigroups: case of Lipschitz nonlinearities. JOURNAL OF EVOLUTION EQUATIONS, Volume 6, Issue 4, pp 711-743. pdf
      31. GOZZI F., RUSSO F (2006). Verification Theorems for Stochstic Optimal Control Problems via a Time Dependent Fukushima – Dirichlet Decomposition. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, vol. 116; p. 1530-1562. pdf
      32. GOZZI F., RUSSO, F (2006). Weak Dirichlet Processes With a Stochastic Control Perspective. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, vol. 116; p. 1563-1583. pdf
      33. GOZZI F., SWIECH A., SRITHARAN S.S. (2005). Bellman Equations Associated to The Optimal Feedback Control of Stochastic Navier-Stokes Equations. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, vol. 58 (5); p. 671-700. pdf
      34. GOZZI F., SWIECH A., ZHOU X.Y. (2005). A new proof of the stochastic verification theorem for viscosity solutions. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, vol. 43 (6); p. 2009-2019. pdf
      35. FAGGIAN S., GOZZI F. (2004). On the dynamic programming approach for optimal control problems of PDE’s with age structure. MATHEMATICAL POPULATION STUDIES, vol. 11 (3-4); p. 233-270. pdf
      36. GOLDYS B., GOZZI F., VAN NEERVEN J.M.A.M. (2003). On the Closability of Directional Gradients. POTENTIAL ANALYSIS, vol. 18, n.4; p. 289-310. pdf
      37. SBARAGLIA S., PAPI M., BRIANI M, BERNASCHI M., GOZZI F. (2003). A model for the optimal asset liability management for insurance companies. INTERNATIONAL JOURNAL OF THEORETICAL AND APPLIED FINANCE, vol. 6 (n.3); p. 277-299. pdf
      38. BARUCCI E., GOZZI F. (2002). Technology Adoption and Accumulation in a Vintage Capital Model. JOURNAL OF ECONOMICS, vol. 74/1; p. 1-38. pdf
      39. GOZZI F., MONTE R., VESPRI V. (2002). Generation of analytic semigroup and domain characterization for degenerate elliptic operators with unbounded coefficients arising in Financial Mathematics, part I. DIFFERENTIAL AND INTEGRAL EQUATIONS, vol. 15, n.9; p. 1085-1128. pdf
      40. GOZZI F., SWIECH A., SRITHARAN S.S. (2002). Viscosity solutions of dynamic programming equations for optimal control of Navier-Stokes equations. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, vol. 163, n.4; p. 295-327. pdf
      41. GOZZI F., VARGIOLU T. (2002). On the superreplication approach for european multiasset derivatives. MATHEMATICAL METHODS OF OPERATIONS RESEARCH, vol. 55/1; p. 69-91. pdf
      42. FRENI G., GOZZI F. (2001). On a dynamic nonsubstitution theorem and other issues in Burgstaller’s “Property and prices”, METROECONOMICA, vol. 52-2, pp. 45-60. pdf
      43. BARUCCI E., GOZZI F., SWIECH A. (2000). Incentive Compatibility Constraints and Dynamic Programming in Continuous Time. JOURNAL OF MATHEMATICAL ECONOMICS, vol. 34-4; p. 471-508. pdf
      44. GOZZI F., ROUY E., SWIECH A. (2000). Second order Hamilton-Jacobi Equations in Hilbert Spaces and Stochastic Boundary Control. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, vol. 38-2; p. 400-430. pdf
      45. GOZZI F., SWIECH A. (2000). Hamilton-Jacobi-Bellman equations for the optimal control of the Duncan-Mortensen-Zakai equation. JOURNAL OF FUNCTIONAL ANALYSIS, vol. 172; p. 466-510. pdf
      46. GOZZI F., LORETI P. (1999). Regularity of the minimum time function and minimum energy problems: the linear case. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, vol. 37-4; p. 1195-1221. pdf
      47. BARUCCI E., GOZZI F. (1999). Optimal Advertising with a Continuum of Goods.  Annals of Operations Research, vol. 88, p. 15-29, (1999). Special issue for the Sixth Viennese Workshop on Opt. Control and Dynamic Games (Vienna 1997). pdf
      48. BARUCCI E., GOZZI F. (1998). On Investments in a Vintage Capital Model. RESEARCH IN ECONOMICS, vol. 52; p. 159-188. pdf
      49. FLANDOLI F., GOZZI F. (1998). Kolmogorov Equations Associated to Stochastic Navier-Stokes Equations. JOURNAL OF FUNCTIONAL ANALYSIS, vol. 160; p. 312-336. pdf
      50. GOZZI F., TESSITORE M.E. (1998). Optimality Conditions for Dirichlet Boundary Control Problems of Parabolic Type. JOURNAL OF MATHEMATICAL SYSTEMS, ESTIMATION AND CONTROL, vol. 8-1. pdf
      51. GOZZI F. (1996). Global Regular Solutions of Second Order Hamilton-Jacobi Equations in Hilbert spaces with locally Lipschitz nonlinearities. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol. 198; p. 399-443. pdf
      52. GOZZI F., ROUY E. (1996). Regular Solutions of Stationary Hamilton-Jacobi Equations in Infinite Dimensions. JOURNAL OF DIFFERENTIAL EQUATIONS, vol. 130-1; p. 201-234. pdf
      53. CERRAI S., GOZZI F. (1995). Strong solutions of Cauchy Problems associated to weakly continuous semigroups. DIFFERENTIAL AND INTEGRAL EQUATIONS, vol. 8 – 3; p. 465-486. pdf
      54. GOZZI F. (1995). Regularity of solutions of a second order Hamilton-Jacobi equation in Hilbert spaces and application to a control problem. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, vol. 20 -5&6; p. 775-826. pdf
      55. CANNARSA P., GOZZI F., SONER H.M. (1993). A dynamic programming approach to nonlinear boundary control problems of parabolic type. JOURNAL OF FUNCTIONAL ANALYSIS, vol. 115; p. 25-61. pdf
      56. CANNARSA P., GOZZI F., SONER H.M. (1991). A boundary value problem for Hamilton-Jacobi equations in Hilbert spaces. APPLIED MATHEMATICS AND OPTIMIZATION, vol. 24; p. 197-220. pdf
      57. GOZZI F. (1991). Some results for an optimal control problem with a semilinear state equation II. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, vol. 29-4; p. 751-768. pdf

 

Papers in refereed italian journals

      1. GOZZI F. (1988). Some results for an optimal control problem with a semilinear state equation I. ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI, vol. 8; p. 423-429. pdf

Papers in International Proceedings

      1. GASSIAT P., GOZZI F., PHAM H. (2015). Dynamic Programming for an Investment/Consumption problem in illiquid markets with regime-switching. “Proceedings of the conference on Stochastic Analysis and Control in honor of J. Zabczyk”, 103–118, Banach Center Publ., 105, Polish Acad. Sci. Inst. Math., Warsaw, 2015. , Banach Center Publication, Poland.PDF
      2. GIULI M., GOZZI F., MONTE R., VESPRI V. (2007). Generation of analytic semigroup and domain characterization for degenerate elliptic operators with unbounded coefficients arising in Financial Mathematics, part II. In: H. Amann, W. Arendt, M. Hieber, F.M. Neubrander, S. Nicaise, and J. von Below, editors; Functional analysis and evolution equations: the Gunter Lumer Volume, pages 315-330. Birkhauser Verlag, Basel/Switzerland, 2007. pdf
      3. GOZZI F., MARINELLI C. (2006). Stochastic optimal control of delay equations arising in advertising models. In: Stochastic PDE’s and Applications VII (Levico  Terme, Italy),  p. 133-148, Lect. Notes Pure Appl. Math., 245, Chapman & Hall/CRC, Boca Raton, FL, 2006. pdf
      4. FRENI G., GOZZI F., SALVADORI N. (2003). Endogenous Growth in a Multi-Sector Economy. In: The Theory of Economic Growth: a ‘Classical’ Perspective, p. 60-80. pdf
      5. GOZZI F. (2002). Second order Hamilton-Jacobi Equations in Hilbert Spaces and Stochastic Control. In: Stochastic PDE’s and Applications (Trento 2002), p. 255-285.  Lecture Notes in Pure and Appl. Math., 227, Dekker, New York, 2002. pdf
      6. GOZZI F., VARGIOLU T. (2002). On the superreplication approach for interest rates derivatives. In: Seminar on Stochastic Analysis, Random Fields and Applications, III (Ascona, 1999), 173–187, Progr. Probab., 52, Birkhäuser, Basel, 2002. pdf
      7. COZZANI V., GOZZI F., MAZZONI A., ZANELLI S. (2001), “Assessment of probabilistic models for the estimation of accident propagation hazards”. Proc. Eur.Conf. Safety and Reliability, MG: Torino 2001; p.807-814.
      8. BARUCCI E., GOZZI F., VESPRI V (1999). A Semigroup Approach to No-Arbitrage Pricing Theory. In: Seminar on Stochastic Analysis, Random Fields and Applications (Ascona, 1996), 1–14, Progr. Probab., 45, Birkhäuser, Basel, 1999. pdf
      9. GOZZI F. (1997). Strong Solutions for Kolmogorov Equations in Hilbert Spaces. In:  Partial differential equation methods in control and shape analysis (Pisa), 163–187, Lecture Notes in Pure and Appl. Math., 188, Dekker, New York, 1997. pdf
      10. GOZZI F., TESSITORE M.E. (1997). Sufficient Conditions for Dirichlet boundary control Problems of Parabolic type. In: Partial differential equation methods in control and shape analysis (Pisa), 189–204, Lecture Notes in Pure and Appl. Math., 188, Dekker, New York, 1997. pdf
      11. GOZZI F. (1996). Alcune osservazioni sull’immunizzazione semideterministica. In: XX convegno AMASES, Urbino, Settembre ‘96, p. 273-290. pdf
      12. CANNARSA P., GOZZI F. (1992). On the smoothness of the value function along optimal trajectories. In: Boundary control and boundary variation (Sophia-Antipolis, 1990), 60–81, Lect. Notes Control Inf. Sci., 178, Springer, Berlin, 1992. pdf
      13. GOZZI F. (1989). Some results for an infinite horizon control problem governed by a semilinear state equation. In: Control and estimation of distributed parameter systems (Vorau, 1988), 145–163, Internat. Ser. Numer. Math., 91, Birkhäuser, Basel, 1989. pdf

Old working papers

        1. DI GIACINTO M., FEDERICO S., GOZZI F., VIGNA E. (2011). Constrained portfolio choices in the decumulation phase of a pension plan. Preprint.
        2. FABBRI G, GOZZI F. (2008). Vintage Capital in the AK growth model: a dynamic programming approach: extended version. Preprint.
        3. FRENI G., GOZZI F., SALVADORI N. (2001). A Multisector “AK Model” with Endogenous Growth: Existence and Characterization of Optimal Paths and Steady States Analysis., Preprint del Dipartimento di Scienze Economiche, Pisa. Working paper.
        4. GOZZI F., MONTE R., VESPRI V. (1997). Generation of analytic semigroups for degenerate elliptic operators arising in financial mathematics. Working paper.
        5. GOZZI F. (1995). Transition Semigroups and Solutions of Kolmogorov Equations in Hilbert Spaces. TUBINGER BERICHTE vol. 4, p. 69-96. Working paper.

 

Didactic Books

      1. CASTELLANI M, GOZZI F., BUSCEMA M, LATTANZI F, MAZZOLI L, VEREDICE A (2007). Precorso di Matematica. BOLOGNA: Esculapio
      2. GOZZI F., CASTELLANI M. (2001). Matematica di Base per l’economia e l’azienda. Esercizi e testi d’esame svolti. BOLOGNA: Esculapio

 

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