Index

admissible controllers, 95

aggregate dynamic financial system, 40

analytical solution, xv, 1, 91, 104-108, 143

approximate solution methods, 10

approximation methods, 11

approximation problem, 12

associated problems, 6, 7

augmented Lagrangian algorithm, 11, 15, 98

bang-bang control, 1, 4, 7, 16, 17, 19, 26, 41,

47, 97, 101

bang-bang optimal control problems, 26, 27, 143

bang-bang optimal control solution, 40 big subintervals, 42-44, 101 boundary conditions, 6, 97 business cycle instabilities, 39

candidate selection systems, 13

cash management, 4

co-efficient, 7, 13

co-state function, 6, 9, 15

computational algorithms, 1, 10, 14, 20, 21, 101

computational experiments, xvii, 36, 89

computational methods, 1, 11, 19, 24, 27, 40,

97, 100, 101, 141 CONMIN, 11 constant-input arcs, 16

constr, 15, 20, 25-28, 44, 45, 102, 141, 189

continuous optimal control models, 10

control, 2, 12-14, 20, 22, 26, 27, 30, 31, 33, 36, 37, 39-47, 54, 61, 67, 86, 88, 103105, 111-113, 115-122, 142

control discretization approach, 10

control function, xvi, 9, 14, 18, 19, 21, 23, 39,

142, 189 control mechanism, 89 control parameterization knot points, 16 control parameterization technique, 11, 12

control policy, 10, 29, 46, 54, 61, 67, 88, 101,

103, 109 control restraint, 95 control strategy, 16 control system, 11, 17 control variables, 93, 139 convergence properties, 12 convex function, 96 cost analysis, 10

cost function, 2, 11-13, 19, 27, 28, 30, 35, 36,

41, 45, 91, 142 cost of changing control, 8, 19, 20, 27, 30, 36,

41, 86, 89, 142 CPET, 16, 19 CSTVA, 19, 139, 141

damped oscillator, 12, 39, 40, 54, 143

damping function, 89 DE solver, 15, 21, 22, 26 decision variables, 13 deterministic, 1, 4, 18 deterministic optimization, 2 difference of optimal control policy sequences, 10

discount factor, 24

discrete optimal control models, 10

discretization augment, 18

division of the time intervals, 10

Dodgem problem, 12

dynamic behavior, 40

dynamic equation, 7, 18, 23, 28, 29, 102, 189

dynamic financial system, 1, 39, 40, 142 dynamic optimization models, 1, 3 dynamic programming, 10, 11

economic models, 14, 15 end-point constraint, 98

end-points, 10, 42, 43

financial decision making, 3, 30, 39, 41

financial engineering, 4 financial market, 89, 92

financial optimal control models, 2, 8, 18, 22,

139, 141-143 financial optimization models, 2, 4 financial planning, 4, 142 financial sector, 39, 89

financial system, 1, 39-41, 43, 54, 88, 102, 111,

115, 139, 142 finite difference approximation, 15 finite difference method, 141 finite horizon models, 4 Fish problem, 12 fishery harvesting model, 12 fitting functional, 21, 30-33, 35, 48, 54, 109, 110,

113-115, 118-122, 139 fixed-time control, 3

fixed-time optimal control problem, 11, 23, 25 fixed-time period, 19 forcing function, 41, 114

global minimum, 5, 10, 18, 54, 116, 122 gradient search methods, 10, 11

grid-points, 11, 14, 19, 26, 29, 31, 45, 102

Hamiltonian, 4, 6, 9, 15, 96

implicit constraints, 14, 15 indifference principle, 8-10 infinite horizon models, 4 initial and terminal conditions, 4 inter-temporal time preference, 3 interpolation, 11

investment, 4, 30, 36, 41, 89, 91-93, 102, 110,

113, 141-143 investment allocation, 91, 143 investment model, 16

Karush-Kuhn-Tucker, 5

Lagrange multipliers, 5, 98, 99 Leap-Frog Algorithm, 17 linear interpolation, 11, 15, 29, 46, 103, 187 local minimum, xvii, 4, 10, 116, 118, 122 low-pass filter, 11

mathematical programming, 4, 94

mathematical structure, 1, 4

MATLAB, xvi, xvii, 11, 12, 14, 15, 18, 20, 2528,44,45, 101, 102, 141, 189

Maximum Principle, 2, 4, 94, 96

maximum principle, 8-10

minimization problem, 2, 4-6, 18, 27, 30, 44, 98, 102

MISER, 11, 12, 14, 17-19

mixed discrete and continuous optimal control problem, 13

multi-state functions, 40

necessary conditions, 6, 17, 96 non-linear complex dynamic behavior, 89 non-linear control system, 17 non-linear transformation, 20, 21 non-smooth functions, 12 nqq computer package, 41 nqq function, 20

obstacle, 18

OCIM, 11, 12, 14, 18

ODE, 15, 19

operations research, 2

optimal consumption, 4

optimal control modeling, 1, 142

optimal control problems, 1, 2, 4, 7, 8, 10-15,

17, 20, 23, 25 optimal control theory, 1 optimal controller, 95 optimal corporate finance, 4, 92 optimal investment planning, 4, 20, 36, 89, 141 optimal investment strategy, 89 optimal path, 18 optimal portfolio choice, 4 optimization criteria, 3

oscillator problem, 12, 36, 37, 40, 44-46, 120,

124, 142 oscillatory behavior, 39 oscillatory dynamics, 39, 89 oscillatory financial model, 39

penalty constant, 13

penalty term, 14, 91, 98, 99, 142

piece-wise continuous function, 2 piecewise-linear transformation, 20, 21, 25, 29, 141

planning horizon, 2, 6, 31, 94, 98, 101

Pontryagin theorem, 2, 6, 8, 9, 18 Pontryagins Maximum Principle, 17

Quadratic Programming sub-problem, 25 quasi-Newton updating method, 11, 25

real-world problems, 1, 2

restricted domain, 18

reverse-time construction technique, 94

RIOTS, 11, 12, 18, 19

risk management, 4

scaled time, 22, 28-30, 42, 43, 45-7, 100, 102,

SCOM, 12, 21, 25

second order differential equation, 20, 39, 40, 45, 46, 141

sequential quadratic programming method, SQP,

20, 25, 141 single-input non-linear system, 16

singular arc, 7, 16, 26, 41, 97

stabilization mechanism, 39

stable optimal investment planning, 89

state variables, 93, 97, 111

STC, 16, 17, 19

step function, 3, 10, 11, 14, 15, 18-21, 25, 26,

40, 120, 141, 142, 189 stochastic, 1, 4, 16, 18 stochastic finance, 4

stochastic financial optimal control model, 18 STV algorithm, 19, 20, 141, 143 switching control, 3, 27, 41, 86, 89 switching time computation method, 16 switching time variable method, 141

switching times, 13, 17, 19, 26, 27, 29, 31, 32,

35, 36, 39, 43, 46, 47, 67, 89

system parameters, 13, 44

terminal constraint transformation, 98

terminal manifold, 94

time optimal control problems, 16

time scale, 23, 39, 41, 42, 99

time subdivision, 40, 108 time transformation, 21, 101 time-optimal control, 3 time-optimal control problems, 23 TOBC, 17 TPBVP, 17

two-point boundary-value problem, 17 valuation, 4